Can you solve the 4 foods puzzle?

Thanks to James W. for the suggestion! At an amusement park, 65% of visitors ate a donut, 80% ate a soft pretzel, 80% ate pizza, and 90% ate ice cream. What is the minimum percentage of visitors that ate all 4 foods?
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[@g.c.9904]

I can never solve the puzzles in the channel because when I open the video the solution is right in front of me in the top comment.

[@thewordsmith7364]

I solved it by inverting the percents (100-p)%, then adding it together, to figure out what percentage at most didn’t eat at least one food

[@Noname-67]

Best solution

[@leonais1]

You can make that mathematically sound by showing that the minimum percentage goes up if there are overlaps between the people who don't eat each food. It's still the best way though.

[@mihailghinea]

same!

[@Sonny_McMacsson]

Or add them together and do (mod 100).

[@danfg7215]

I did the same thing and arrived at 15%, but since I did it "intuitively", I didn't have confidence in the result.

[@Yusso]

I did the second method but then I realized it's easier: Assuming that there are 100 people and no person ate the same item twice. If all of them ate all 4 items there would be 400 sales. But if we add up the numbers there has been 315 sales. So at most 85 people did not eat all 4 items. That means at minimum 15 people ate all 4 items.

[@metamud8686]

> no person ate the same item twice. The thing is, in the problem description this is left implicit. Somewhere while explaining the answers, this assumption was suddenly put into place. Before that, nobody excluded a person eating, say, 4 slices of pizza.

[@Yusso]

@@metamud8686 Right. But maybe it's not important how much one person bought of each item. So for example if a person buys 1 donut or 10 doesn't matter. The question then would be, did they buy it or not.

[@XTheSoccerLoverX]

Seems like a great problem to illustrate key ideas like DeMorgan's law and the Union Bound, but I don't think the connection was made as clearly as it could have been. There's a lot of intuition that was brought out be each solution, I think the connection to formalized concepts could have been a lot stronger.

[@swordgeo]

I tried at first to follow the method of option A with weird bar graphs but gave up and found myself doing naturally going with option B. I wondered if I had the right idea pairing donuts with pretzels and pizza and ice cream but it seemed to make sense to me. And I'm glad the video showed that I was right!

[@ShawnF6FHellcat]

I either got lucky or found a much easier way to do this: -Adding up the percentages of those that didn't eat each food equals 85%. -Subtract that answer from 100%, which equals 15%. I can't explain why that worked, but it apparently did.

[@GS-td3yc]

i took two items and took the inverse of the bigger and subtracted from the smaller. substituting the result and repeating yielded 15 percent. after i saw that any order yields the same solution, i am pretty confident

[@kalan4787]

Intuitive answer is 15%. There is an algorithm to execute which makes this exceptionally easy. Basic description: You take the two lowest percentages to start. You have to calculate their intersection so that is going to be 65-(100-80)=45 then you take that answer and intersect the 3rd. 45 - (100-80) = 25 Take that number and intersect the 4th. 25 - (100-90) = 15. Done; it should take you approximately 3 seconds to do in your head. Algorithm: var accumulator = 0 foreach(var p in list){ if accumulator ==0 accumulator = p else accumulator -= (100-p) } accumulator will contain the intersection as long as there is one. A defense is necessary to prevent a disjoint set from resetting the accumulator to a positive number, but I'm not presenting this as a general solution to the problem of all intersecting sets. You have to sort them lowest to highest. It would have been a better problem if he had presented them out of sort order

[@matthewwriter9539]

I just saw a video with a math puzzle on it. At the top of a paper write "I have $50" Now divide the paper into two columns, Spent Balance 20. 30 15. 15 09. 06 06. 00 For each of these you spend some amount of money, then you write your new balance in the balance column. Now total up each column. The spent adds up to 50, which we expected. Yet the balances all add up to 51...where did that extra one dollar come from?

[@Tanuvein]

All these puzzles are so fun

[@kurax9115]

A more visual, but also odd way imo is the following: Imagine a line of 100 people standing from left to right. Now take any of the number of percentages from above, say 80% (pretzel) and color the people from left with yellow. Now, take, say 90% (ice cream) and color the people from right with blue. The overlapping amount of people will be the ones who at minimum ate both pretzels and icecream, which is 70 people. Do that again with the other numbers and you will end up with 15 people = 15% This is by far more complicated than it should be but its the first idea that came to my mind because i wanted to visualize it. Edit: I wrote this comment before watching the video.

[@UnicornedBatman]

I think it would be 65% at the most and 15% at the least

[@donsimon2830]

I can imagine an ice cream donut and a pretzel pizza but not the ones you imagined.

[@TerjeMathisen]

This seemed hard for a few seconds until I realized I could invert it. 🙂

[@sunnicivang1093]

I was mentally thinking of Method 2, but was physically trying to write it out using Method 1, and using 100 people.

[@HassanAhmed-bs5fn]

First: 90% vs 80%, the 10% that didn’t eat from the 90% could of ate part of 80% Thus, there is a minimum of 70% overlap Second: 80% vs 80%, since one of the 80% has a 70% overlap from before, 30% of the people who didn’t overlap could of ate from the other 80% Thus, there is a minimum of 50% overlap Third: 65% vs 80%, since the 80% has a 50% overlap from before, 50% of people who didn’t overlap could of ate from the 65% Thus, there is a minimum of 15% overlap. Didn’t see many people point out the logic, hope this helps.

[@benismann]

I hate how you didnt include "minimum" on the thumbnail and i had to be confused by it being literally unsolvable

[@gautamsaha9397]

Another way to solve. The percentage who didn't take the food is 35+20+20+10=85 So all food are taken by 100-85=15%

[@chewy560]

Having eaten all for foods I can confirm the ice cream was my favourite.

[@BeefinOut]

The real question is, why is everyone eating so much food? The median guest ate at 3 distinct food stands during their trip, that's nuts

[@PythonPlusPlus]

Given that they could just be getting a drink or a snack, it’s not crazy that they could be visiting 3 food stands in a day at an amusement park.

[@chinareds54]

The real world conclusion of this story is that the amusement park sells the bundle and finds out that much lower than 15% buy it (probably even less than 5%). The reason being human behavior; no one wants to eat all four at the same time. Even if the bundle were like coupons to be used throughout the day, most people don't plan on eating all four of those items and/or are hesitant to part with their money up front to commit to eating all four. They'd rather just spend their money at POS when they have a craving for something.

[@gemstonegynoid7475]

Yeah. This is two mains and two desserts. A person might like a deal for one and one. But not all four.

[@KroganCharr]

The bundles might be interesting for groups that share the food. I don't think it's a very popular idea anyway, though. A third of the people in this scenario apparently just don't like donuts, so they will be skeptical with a bundle that forces them to buy one.

[@macdavidson3814]

My method was similar to the first one. I thought "What would people have to do in order to get these numbers with the least people getting all 4?" And the answer is everyone who didn't buy 4 is buying 3 items exactly. So I'm assuming that everyone who didn't buy ice cream bought a pizza, a pretzel, and a donut. And everyone who didn't buy a pizza bought icecream, a pretzel and a donut and so on. So I took the inverse of every percentage and added them up since assuming everyone is behaving this way, they are mutually exclusive combinations. They added up to 85%. So 85% of people could buy only 3 items and still get these percentages, so the remaining 15% have to buy all 4.

[@plasmaastronaut]

that was easy. i found the answer in my head after 30sec thought and i'm average at these puzzles.

[@matthewwriter9539]

...actually I had two donuts, three pretzels, one slice of pizza, and two ice cream cones.

[@SerifSansSerif]

OK. Before watching, I thought about it and I was trying to come up with ways to figure out overlap. So if 90% of people ate one item, then only 10% ate something else. Those 10% could have been the people that ate food B, alone, and 20% of those that didn't eat B would have meant only 70% overlap. So 90%=10 80%=20 80%=20 65%=35 10+20+20+35=85. There's at LEAST 15% that ate all four foods

[@kardelenkoc9746]

i had similar question for a big test that we had in turkiye which determined where i could study in highschool and i couldn't solve it i still can't and i don't think i will ever. my dad told me to do the "imagine if everyone ate 3 of those" technique too

[@christinae30]

I thought about it for 20 - 30 sec, no calculating (except adding four numbers). Same result as video got. Now I feel intelligent. Nice😉

[@Hanible]

I instinctively did sum mod (100) = 15 so 15% and I thought of putting the 2 foods together in a new category that's the intersection of both!

[@FlyingFox86]

"Let's imagine there are 20 people..." Why on Earth did you not go for 100 people?

[@blastygamez]

Can you make a formula of this? I thought it was: summary of the percentages and then applying remainder/modulus 100 which did get the answers but when there aren’t any 100’s in the sum then u get something impossible sum 1% donuts, 1% pizza. Modulus(sum,100)=2?!

[@Xanderbelle]

That's the first time I've seen Venn diagrammes made usefull

[@ljsd1]

I basically used method 1, using a 1-100 number line.

[@aba_dab_o]

Solved it through Method 1. Still trying to wrap my head around the Method 2 venn diagrams, although the Minimal Proof helped it. The Possible trick? is an intriguing and plausible method.

[@rivers4753]

My intuitive guess was to imagine the 65% and the 80% filling a bar from opposite ends. Because 65% definitely ate doughnuts, and 80% definitely ate pretzels, then the overlap is the minimum people that ate both. Doing this for pizza and ice cream will net you the same number or higher so it had to be 15. Also side note, I just realised typing this out, this is my exact mental method for solving those nonogram puzzles

[@omnipotentpotato2436]

Yeah did the same as you

[@MrMousley]

Take the lowest percentage .. 65% .. and now work out the 'did not eat' percentage for the other three .. 20% twice and 10% once .. add them together .. 20 + 20 + 10 = 50 .. and now subtract 50 from 65 .. giving you 15 .. and telling you that the minimum number of people who ate all four is 15% .. going up to a maximum of 65%.

[@taichivillaruel9114]

Here's how I solved it: *I took 100 people as a sample size to make the calculation easier. I took the 90% first, then that means 10% of the people didn't eat ice cream. *I took the pizza slice(80%) next, then that means 20% of them didn't eat pizza slice, and I carried over the 10% from earlier to here, so that means 30% neither ate the pizza slice nor ice cream(or both). *Same process with the donut(20%). That means 20% of the people didn't eat donuts and I carried the 30% from earlier again here. That means 50% of people didn't eat at least one of the following: Donuts, Pizza Slice and Ice Cream. *Finally, I took the pretzel(65%). That means 35% of the people didn't eat it then I carried over the 50% of the people from the previous proposition. That means 85% of people didn't eat at least one of these 4 items. That leaves me 15% of people who ate all of these 4 items. I don't know how this works, but hey, I got the correct answer and that's what matters. 😅😅😅 On a side note, I realized that 100 people isn't necessary here. 😂😂😂

[@taichivillaruel9114]

Sorry. I inverted the donut and the pretzel, but you get the point. 😅😅😅

[@keith6706]

Well, there's on thing this "too simple problem" (as some people have complained about) demonstrates: people will argue that the correct answer is wrong even when their own eyes can see otherwise. That, or they don't understand what "percentage" means.

[@antoniozumpano826]

Look at that: 35 = no (a); 20 = no (b); 20 = no (c) and 10 = no (d). So, 35 + 20 + 20 + 10 = 85 persons who do not eat at least one of the four types. Thus, (a), and (b), and (c), and (d) do not belong to this set of 85 persons. Therefore, 15 people eat all four types. The union of the four sets may be less than 85. So, the complement may be greater than 15. Therefore 15 people are the minimum.

[@aslmj2]

I just took the minimum percentage of 65 and subtracted remainings of others like 20 from 80 20 from other 80 and 10 from 90. Got 15

[@to2burger]

I guess technically the answer would be somewhere between 15 and 65 percent because you can’t really know for certain with such limited info- but for the sake of the logic problem, yes at least 15 percent ate all 4 foods. Example of how to solve the problem “it’s possible that the 20% that did NOT eat pizza DID eat donuts, so we can remove their 20% from those who ate ALL 4 foods”. 65-20 = 45% then repeat this step in the problem for the for the other two foods and you get 65-20-20-10 = 15 (start with the donut value and subtract the DIFFERENCE between the other percentages of foods eaten and 100%. This tells you the lower limit of AT LEAST what percentage of people MUST have consumed all 4 foods - because that lowest percentile MUST apply to all 4 groups. This will tell you the POSSIBLE percentage of people that MIGHT have eaten the other 3 foods, but not the 4th. It is 50% that might not have eaten 3 or less foods, but not all 4. And so the most accurate answer would be a range of somewhere between 15% and the full 65% because albeit unlikely, you can not rule out that everyone who took a donut also took the other 3 foods as well. Highly unlikely maybe but still likely.

[@SioxerNikita]

The answer is 15%, because it is the MINIMUM amount of people that have eaten all four foods. Not "How many did".

[@Sh1sou]

The last equation in simple: answer = 100-(100-w + 100-x + 100-y + 100-z)

[@madisonking8057]

This kind of problem will be very familiar to anyone that has taken a genetics course.

[@scoorp8]

Okay but this is assuming that all visitors ate at least 1 food item and ignores the possibility that possibly up to 10% of people had nothing to eat.

[@WombatMan64]

Not really. If you introduce additional caveats that some people ate nothing, then work through the numbers (or diagrams) again, you actually end up with more than 15% now must have had all four. So the minimum (15%) occurs when everyone ate at least one item, as any new constraints increases that number.

[@happinesstan]

I'm guessing you start by collecting the 4 100%s to give a relative figure of 400. Then you add up the individual percentages, giving a total of 315. Subtract that from 400 and divide by 4? So the minimum percentage would be about 20.125%. That's a rough guess. EDIT: I see I was wrong, but in my defence, I would argue that your answer is less accurate to the truth. It answers the question of course, What is the lowest possible? But it's probably wise to dismiss that as quickly as you would dismiss the 65% maximum.

[@davidcarter8269]

I solved this problem correctly using a different method, lost confidence in myself assuming I was wrong, and then was pleasantly surprised we got the same answer

[@davidcarter8269]

@@thomasmaughan4798 Yes of course getting the same answer isn't proof of correctness, but in my statement when I said "solved this problem correctly" it was implied that I did a correct method. I can show you the method I used if you would like and you can evaluate if it is correct?

[@thomasmaughan4798]

@@davidcarter8269 It appears I answered a question not precisely asked and i'm still thinking about it. Is it possible to insist that at least 15 percent of all visitors *must have* eaten all four foods? It is easy to show that up to 10 percent may have eaten nothing! But that's the other end of the stick. One end of the stick says from zero to 10 percent may have eaten nothing. But the other end says 15 to 65 percent ate all four.

[@leif1075]

PRESH QUESTION I hope you can PLEASE ANSWER for once. Your last method at 6:11 doesn't prove 15 is the minimum or show why 3 foods would becdivided evenly or if that's thecsimplest case. Is that not right? Could you correct this or correct me if I'm wrong?

[@wombat4693]

and here i was trying to figure it out using karnaugh maps lol

[@HaranYakir]

Now solve for what is the most LIKELY number of people who had all 4 and what is the probability of this most likely outcome

[@Quiet704]

Just figure out the max number of people who didnt eat to figure out the minimum amount of people who ate.

[@KataisTrash]

Haven't watched the video solution methodology yet, just checked if my result was right. The way I did it was: 1. Assuming 100 people (to make it easier), A=65, B=80, C=80, D=90. 2. How many people have NOT eaten a food? !A=35, !B=20, !C=20, !D=10. 3. Now, I compared A & !D. If A has 65 people eating it, but only 10 people did not eat D, that means that 65 - 10 people ate both A & D. So, A & D = 55. 4. I do the same for B & !C. If B has 80 people eating it, but only 20 people did not eat C, that means that 80 - 20 people ate both B & C. So, B & C = 60. 5. Lastly, I compare A & D with !(B & C). 55 people ate A & D, while 40 people did NOT eat B & C. That's 55 - 40 = 15, so 15 people ate all four foods. 15 / 100 = 15%.

[@KataisTrash]

@@thomasmaughan4798 Yeah I think 10% could've eaten nothing, but since the question only asks for who ate everything, I didn't look at the ones that ate nothing :)

[@jastopherchristie7288]

Bit have you thought about the way I got it: just a complete guess and being shocked when it turns out i was right?

[@Joel_Nilsson]

Me doing the math of just multiplying with 2 different methods and not even getting close to the correct answer... Method 1: Multiplying all percentages together to get some kind of an average or a likelyhood of someone eating all 4(not sure what I thought this would be). 0.65x0.8x0.8x0.90 = 0.3744 = 37% Realised as soon as I saw it this would be wrong as it's way too high. Method 2: Seeing every food as something u either get or don't therefore a coinflip. 0.5x0.5x0.5x0.5 = 0.625 = 6% Me not being too hopeful about getting it right but still thinking this result made some sense compared to the other and therefore might be correct.

[@alf8988]

Why not just grab the two lowest percentages and get the overlap? 80-65 = 15%

[@FlorisDeLeeuw]

i usually don't get the solution to these puzzles. I got this one in under half a minute, no hard or multilayered calculations needed. I question whether this puzzle is worthy of this channel.

[@Misteribel]

Not seeing the answer yet, but just add the missing people of each percentage: 35% + 20% + 20% + 10% = 85%, so 15% ate all (minimal). I'm not sure why this is supposedly tricky, watching now to see what i missed 😅

[@zaksmith1035]

I solved it by eating a crap ton of unhealthy food, then weighing my next bowel movement. 15.

[@x_mau9355]

This is very good content

[@TxHornyToad]

Anywhere from a minimum of 15% to a maximum of 65%.

[@climbscience4813]

Before I watch the video: Statistically it should be ca. 29% (0.8x0.8x0.9x0.65). However, it could be anywhere between 15% (100%-(20%+20%+10%+35%)) and 65%. Let's see what the video says. 🙂

[@volarantoes]

I got the wrong answer by guessing 65% of people ate all the food

[@nozack5612]

One complaint. I tried to solve via the thumbnail. The thumbnail asks 'How many ate all four foods' not 'What is the minimum number that ate all four foods'. Those are different questions and could have a different answer. There is no answer for the first beyond somewhere between 3 and 13.

[@gergelyritter4412]

I hate Venn-diagrams with a burning passion. If I ever get the chance to wish for smth from a genie, I will get rid of them forever.

[@samcurtin3562]

How people initially thought the answer was 37.44%? (0.65*0.8*0.8*0.9)

[@josiahkalousek2435]

Hi Presh, great video! I got a different answer than you did. I'm sure that you are correct, since this is what you do for a living, but I was hoping that you could explain why my method is innacurate. My method: The liklihood that an individual purchased a donut AND a pretzel AND a pizza slice AND an ice cream cone. The logical "AND" operation is equivalent to the algebraic multiplication function, right? So I multiplied all of the percentages (0.65×0.8×0.8×0.9=0.3744). My answer came out to 37.44%, why is my method innacurate? Was I on the right track at all? I appreciate your time. Thank you for contributing to these videos.

[@WombatMan64]

Hi Josiah, Your method calculated the expected, or average, number of people who ate all four. Probably a more useful piece of information for the marketers; but that's a separate issue. The question was what's the minimum number of people who ate all four. What's the smallest number of all four item eaters that still satisfies the 65, 80, 80, 90 numbers. TL/DR, you got the middle of the bell curve, the question is asking about the left tail.

[@josiahkalousek2435]

@@WombatMan64 Cool! Thank you so much!

[@theeraphatsunthornwit6266]

Min is 15 Max is 65 Expected value is 37.44 percent

[@gap-18mathematics46]

Mr presh...How to solve this equation: x^2+2ln(x)+2=0. Thank u.🌷

[@vladimirfokow6420]

uhm.. can't you just 0.65 * 0.8 * 0.8 * 0.9 = 0.3744 since they all are independent variables, and we're solving for AND ? - ah, got it. 0.3744 is the probability of a random person to each all 4 foods. So this is the expected share of people. Not the guaranteed one.

[@tmGrunty]

Can't you just add up all the percentages all items and then substract 100% * (amount of items - 1)? 65% + 80% + 80% + 90% - (100% * (4-1)) = 315% - 300% = 15%

[@GS-td3yc]

15 percent?

[@kingvax064]

I multiplied 0.65 by 0.8 by 0.8 by 0.9. Why doesn't that work?

[@earthbind83]

4:45 Gross! At least rearrange them to Pizzapretzel and Icecreamdonut!

[@hehehehehehehahahahaha]

i don't get it why can't the minimum be 1 😥

[@Zett76]

At long last, I got one right, within seconds... :D

[@frankvucolo6249]

Great solution. But when I paused to ponder, I kept getting hung up on the up to 10% of people who could have chosen to eat nothing. Perhaps the question could have been phrased, “Of the people who chose to eat something…” Or am I missing something? (probably)

[@SgtSupaman]

Because we are looking for the minimum overlap, we have to assume everyone ate something. If any percentage didn't eat (which is a possibility), then the amount that ate all four is already more than the minimum.

[@SgtSupaman]

@@thomasmaughan4798 , no, you are misappropriating that percentage. The question is about the minimum that ate all four items. If 10% ate nothing, then the items would be overlapped on the other percentage even more. This would RAISE the amount of people that eat all four items. Allow me to reduce it to just 3 people and 2 food items. If you hear that 67% of the people ate item A and 67% of the people ate item B and you want to know how many people had to have eaten both items, then you must consider it like so: item A was eaten by person 1 and person 2 (67%) item B was eaten by person 2 and person 3 (67%) The overlap is 1 person, so at least one person had to eat both items. If you assume that the other 33% ate nothing, then it works out like this: person 1 ate nothing (33%) item A was eaten by person 2 and person 3 (67%) item B was eaten by person 2 and person 3 (67%) Now the overlap is 2 people, so 2 people ate both items. This is not the minimum. By saying any person didn't eat, you increase the amount of people that had to eat all the items, thus, you defeat the purpose of looking for the minimum.

[@thomasmaughan4798]

@@SgtSupaman Good explanation. It also explores why NOT overlapping the non-eaters is important to finding that minimum. If the non-eaters overlap or are the same person, then the poly-eaters must increase their eating. This was a thing not evident to me watching the video. I could see that an assumption was being made, that the non-eaters were distinct and not overlapping, but why was that assumption being made? Your explanation is sensible.

[@screechingtoad2683]

My guess before the answer is revealed 37.44% Edit: i got to that answer by taking 80% of 65, then 80% of that, then 90% of that

[@sandpiperbf9767]

Idk why this works, but I added up each pair of percentages then subtracted off 100% each time, before adding the next pair. I got the correct answer of 15% edit: I guess this is just a venn diagram without drawing the venn diagrams

[@chinanumberone7723]

At least 3/20 so 15%

[@sunkhirous]

Should be around 37%

[@phantom715]

These solutions seem way over-complicated. I started with the donuts. 65%. If 20% didn't have a pretzel, then 65-20=45% had a donut and a pretzel. Then repeat. 65-20-20-10=15% had all 4 items.

[@whyisntfauciinprison2192]

15%

[@kristofclaus7460]

Why not just do 65-20-20-10? Literally took 5 seconds to solve

[@svg3414]

What is the expected number of people who ate all four food items?

[@RoderickEtheria]

90-20-20-35=15% at least.

[@lawrencejelsma8118]

The minimum is 0 because me and my friends bought all the donuts at the park and ate them up getting sick on eating all those donuts not hungry to eat any or all the rest. So union of our group who ate all the donuts with the percentages of people who could only buy pretzels, pizzas or ice cream only also not eating all four food items will be 0 all thanks to me and my friends being donut hogs! 😋

[@soupsundying]

Am I the only one who thought the answer was 65% x 80% x 80% x 90% = 37% ??

[@fabrizioriva1281]

Last one was a bit too much for me

[@cheeseboi8769]

hey, can someone explain why multiplying all the percentages is wrong so 0.65 x 0.8 x 0.8 x 0.9 = 0.37??

[@SioxerNikita]

That's the probability of an individual having eaten all four.

[@WombatMan64]

That gives you the expected number who ate all four items, not the minimum number. Example to illustrate: If you roll a 6 sided die 10 times; your expected total (which you'd probably be quite close to) is 35; but you could theoretically roll a total of 10, which would be your minimum.

[@SioxerNikita]

@@WombatMan64 Technically, it is the probability of an individual having eaten all four, but since everyone is an individual with equivalent chance, it also translates to the expected number, yes XD

[@ForeverHobbit]

i just did 65-(20+20+10)

[@reldahr01]

37.44%?

[@-Katastrophe]

Bruh. who the hell wouldn't eat a donut?

[@aroundandround]

The thumbnail didn’t include either of the two words “independent” or “minimum”, and should have. I’ll still give you a click to check my answer but like to solve it in my head before clicking.

[@thatonefrenchguy937]

15%?

[@Hello_World_not_taken]

37%?

[@Elongmusk420]

atleast 5% ate all foods just saying

[@wild_insomnia]

nice,an ad about constipation medicine popped out.KZbin is hopeless...

[@edsimnett]

What's the logical connection between how many people are interested in the bundle and the minimum number of people that must have eaten all foods? In particular why is the minimum a helpful number to know? To me the interesting question is what the chance that any given person ate all 4 (which is quite a different number, 37.44% I think). Also- this is an odd business strategy as @kroganCharr pointed out- what you really want to know is how many people on average ate any three and might be enticed to buy a 4th for a discount, and would that make money compared with the current expected revenue. So maybe the expected overlap is helpful? On the data presented it would appear that we might want to offer a discount on a doughnut to people to bought an ice cream, because 35% of 90 (~33) people are in that group, but you should probably never try to incent ice cream purchases, because you get them anyway. [grumble- it's a shame when the story gets in the way of the fun math, but sadly they often do]

[@aditya37mviews3weeksago3]

3:56, where are the people that did not eat either of the two(donut or pretzel)

[@Dragoonking17]

Kind of proud of myself. I didn't even need to pause the video for this. I solved it while you were still asking the question.

[@KroganCharr]

For the practical application, you actually do NOT want to target the people who bought all 4. Bundles are typically cheaper than the sum of the individual items - that's the point of the bundle. If we only sell the bundle to people who bought all 4 anyway, we just lose money. The people we ACTUALLY want to target are the ones who bought less, but might be convinced to buy all 4. Most likely, the people who usually buy 3 out of 4 could be tempted by a bundle offer. The donut merchant would be the most likely to profit from this, as most people who only skipped out on 1 probably skipped the donut.

[@TheBlobik]

The information request is still useful though. We know, that with such bundle we loose with at least 15% of the customers, and up to 65%. So, looking for info about people who bought all 4 makes sense, but we should focus on the maximum number of people who did that. Then we can set up the pricing in such way, that even in worst case scenario extra spending of the part of 35% of customers will make up for the loss on 65%. This is of course a "safe bet" scenario, most companies probably could tolerate some risk and look for "most likely % of people who bought all 4" to use in estimations instead.

[@willguggn2]

@@edsimnett The four numbers most certainly aren't independent variables. People have preferences and don't truly randomly buy food in the real world. Upper and lower boundaries however still apply.

[@Tiqerboy]

You also have to measure the time people bought items. If people bought all four at once or 3 items at once (usually a family) that's different than an individual buying all four items but over a longer period of time.

[@DemPilafian]

Keep in mind that the *_"geniuses in marketing"_* was meant sarcastically.

[@Patrik6920]

@@willguggn2 true, and for a small sampling ..not very informative ..but on a larger sampling .. the errors smooth out... as in the exaple lets assume 20 ppl...the variance from day to day will be massive if we say saple 20000/day for a week ... i would say the error becomes so small .. we can with a quite high degree of certainty predict the sales... in the future... and what prferences ppl have .. we can then add other factors as weather, pricing etc... ...we can also just by using common sense do estimations (if its 10 deg and windy, the probability our outdoor ice cream stand sell alot of icecream is quite low)

[@ZekeRaiden]

Minimum percentage can always be determined by picking the lowest percentage (in this case, 🍩 at 65%), and then subtracting away all the "did not eat X" percentages. In this case, those are 20%, 20%, and 10%, for a total of 50%. 65% - 50% = 15%. The actual amount that ate all four items is probably higher, up to maximum of the lowest percentage, 65%.

[@knoxiegb1782]

Yeah I remember being in school and struggling with a variation of this problem. Is there any flaw with that reasoning?

[@opinionhaver574]

That's how I solved it.

[@emulgatorx]

You don't have to start with the lowest percentage, any of them work as a starting point.

[@ZekeRaiden]

@@knoxiegb1782 Formally speaking, what I did was just a specific application of the proof given near the end of the video. The union of WXYZ is no smaller than the whole space (100 percentage points) minus the complement of each individual set. Thing is, (whole space) - (complement of set W) = the set W, by definition. You can, as other replies have said, pick any starting point. I just find it most natural to start from the smallest one first.

[@donaldhobson8873]

max(0,100-sum(100-x for x in percentages)) simpler.