Probability using combinations | Probability and Statistics | Khan Academy

[@niyr419]

Thanks Khan , u the only math mentor that makes sense to me . U get through to many kids , you're a blessing .

[@emmanuelwilliamquinton9152]

It took me a while to understand why he took the number of combination and not permutation. While in the video he goes very fast over it, it is not necessary very instinctive. And especially for people trying to learn statistics I feel it's important to understand clearly why choice of formulas are made.

[@Mo0m0oSaZn]

Wow, seriously that was such a great explanation of how to use the concept of combination in probability. I don't think I've ever seen anyone breakdown the intuition of the factorials. So awesome, thanks Khan!

[@eatbreakfasts7993]

If someone has to say "hopefully I didn't confuse you" THREE times within a nine minute explanation, it probably wasn't that great of an explanation.

[@chopper84a]

so adding the 'multiply by K!' to the bottom is what turns the permutation formula into a combination formula?

[@Slender00000-o]

yes❤

[@MrPlausibleDenial]

Using the binomial distribution to solve. P(n,x) = nCx * P^n (assuming fair coin), P(8,3) = 8C3 *(1/2)^8 = .21875

[@Asmor]

@aew782 Subtract the same number from the exponents on both the top and bottom. Just to keep things clean, let's say it's just 2^3/2^8 = 2^(3-3)/2^(8-3) = 2^0/2^5 = 1 / 2^5. Another way to understand is to expand them out. 2^3/2^8 = (2x2x2)/(2x2x2x2x2x2x2x2). Then you just cancel top and bottom and you're left with 1/2x2x2x2x2 = 1/2^5 Hope that helps!

[@vineetdeepika]

@Su Won Lee , Multiplication by 1/2 is done only to find the probabilty of events in a ROW. or one after the other but here the combination method is used to find the probabilty of events happening in any order like i toss a coin 5 times and get heads the 1st,2nd and 3rd time or get heads 1st 3rd and 5th time ; it doesnt matter how i get heads but it matters that i get it exactly 3 times out of the five. and that is what the combination method is used for!

[@warpiwarpi3533]

Thanks for yet another great video! However, at 8:32, Sal writes and says equal to, where it shall be approximately to.

[@zeusushh]

14 years later and I'm here watching this for my exams

[@bobby123greenhalgh]

Also just a quick tip for all those out there that don't want to simplify factiorials 8!/3!= 8C3 which is a shortcut on many scientific calculators.

[@safwankhan199]

Sal Khan can explain like a mathematician, I can imagine him explaining things to classmates. It makes sense why he is the god of probability.

[@sachinpednekar6929]

You are an awesome teacher! Take it from one of the worst math student! 😊

[@chenadam6339]

the question that Sal mentioned at 9:02 : 2 out of 100 head. P(2/100H)=(100!/2!*98!)/(2^100) the answer is roughly 3.9*10-27. it's almost impossible to occur! is my calculation correct???

[@ZHAOFEIXIANG]

tnnx for the tutorial mate, helped alot

[@colinwelch5749]

Thank you so much. I have a prob test tomorrow and this cleared every ting up for me!!!

[@nightmare4eVerr1]

the question would have said then "probability of getting 3 consecutive heads" "exactly 3 heads" means the combination can be of any order (as sal has done) but it should not exceed or be lower than 3

[@natymartinez3601]

This was super helpful, I was lost when my teacher taught it but I get it now. Thanks.

[@zsomborczoma]

7:58 - Who else said "Yes" when he asked, is that right?

[@swfsql]

Thanks! This wasn't intuitive to me before I saw your explanation! So in terms of chairs.. For the # of 3 heads, the way to think of this is that each coin toss is a person (A,B,C,D,E,F,G,H) and you're gonna select 3 persons to sit on the "3 heads chairs", and since you only care about their selection and not their arrangement, you do 8P3/3P3. Also this should be the same as selecting 5 persons to sit on the "5 tails chairs", in which case you'd do 8P5/5P5, which is the same result.

[@SubZero90Gaming]

Thank you, very helpful!

[@tharunishadi3980]

probability is easy for me now.. thanks to you...thank you sir!

[@Musicjuice12345]

Thank you sir😮

[@Roleplayer40K]

Assuming this is true, then 5 heads out of 8 flips is also 21.875% chance of occurring. Another problem also happens when you flip a coin 4 times and want head 3 out of those 4 flips. Using the tree method the result is 31.25% but using this method the answer is 25%

[@understandingmaths1033]

You are correct that the probability of 5 heads is also 21.875%. It's not so surprising if you visualise the distribution curve, which has a classic symmetry. The tree method for 4 coin tosses should identify four pathways: THHH, HHTH, HHHT or HTHH. Each of these has a 1/16 probability, so adding these together equals 4/16 = 0.25 (25%). Hope that helps!

[@TasyaAdzkiya]

Correct me if I'm wrong, but I THINK the reason why the formula of finding the probability of (in this case) 3 heads out of 8 coin flips = (the total number of groups of 3 heads of 8 coin flips, which fits our constraint because we want to know the probability of getting 3 heads out of 8 coin flips)/(the total number of possible outcomes) is because it's just the same as other probability formula. Plain ol' probability formula. The numerator, which is the number of POSSIBLE events that fits our constraints (which, in this case is the number of groups of 3 heads out of 8 coin flips) is divided by the denominator, which is the total number of possible outcomes. To find the number of events (or in this case, the number of groups of 3 heads out of 8 coin flips), we use combination because we don't care about the orders. We only care about specific combination of 3 heads from which coin flips (is it the 1st coin flip that result in head, and so on) is in a group. And those groups of 3 heads are just the possible event that we may get, which means that if we were to win 3 heads out of 8 coin flips, we will get one of the combinations of groups of 3 heads (which, in this case, there are 56 of them). (It's just my assumption, correct me if I'm wrong) It's similar to the probability of getting 1 green ball out of 3 green balls and 2 yellow balls. It would be 3 (the total possible events that fit our constraints, which are the green balls)/5 (the total of all possible events/balls that we may choose).

[@saithiha525]

Thanks Mr. Khan! it helps me a lot

[@atomikrobot300099]

You can your binomPDF( function on your "average" graphing calculator to do this @8:51...

[@LazLoGirL]

..this actually helped.. thank you :)

[@burnsyy9119]

The probability of getting a head is 1/2.Where does that fit into this formula?

[@VndNvwYvvSvv]

Is there a different way to approach this that's more intuitive? I know there are at least 2 ways. Adding a second method woudl double the approaches

[@VijfMiljard]

In a previous vid Sal talked about putting n people on k chairs. I think he should gave followed that logic here. Placing 8 people in 3 chairs is similar to distributing 8 flips over 3 heads. That is, if you don't care about order.

[@davidmartin123]

Yes, you confused me. Too many extraneous analogies e.g choosing people in a car. Confine your narrative to the specific problem statement domain (coin flips).

[@trevorhawke8183]

I LOVE THIS

[@sharastar8806]

Trevor Hawke my son

[@majidsheraz8098]

Thank you Khan Academy

[@bobby123greenhalgh]

ask your teacher at school how to do probability trees, You can solve this problem using probability trees as your method.

[@dhanushronaldo5378]

For ESC512 exam you have a list of 10 problems and you may solve 6 of them. However, for the exam I am going to use at random only 5 problems from the list I provided. What is the probability that you may solve all 5 problems from the exam?

[@srinalla6328]

thanks

[@PriyanshuKumar-wc4vh]

Boy Permutations and communication is making probability tough.

[@m3tm4n]

Can you calculate the total outcome with the combination formula??

[@deepkushagra]

How do I decide which is n and which is k where am I going wrong when I say - there are 8 slots and 3 Heads have to fit in those. So, n=3 and k=8

[@khadijahflowers5566]

This is sort of late, but when we look at which numbers to assign to 'n' and 'k' we look at what we are choosing out of. In this example we wanted 3 Heads but we have 8 possible points in our experiment where we could get Heads, but we only want 3, so since we are choosing 3 things from 8 n = 8 and k = 3. I try to think of it as "I have n items, but I only want k of them. So out of these n items, I'm choosing k."

[@GabrielFrosty]

I'd love to know if mtshibingu is right in his factorial calculation?

[@thedisguisedmaster]

Ok, now I got combinations. During the combinations video I was totally confused.

[@raborarmatthewghie959]

thank you so much😁i think i could pass my exam tomorrow*😁*

[@maxspringfield]

there are 'factorials' now?

[@nongthongbamkishan54]

thank u sir!!!

[@polaroidfair]

who noticed that this Sal guy teaches everythg..maths, physics? i noe i did

[@Fall7timestandup8]

Sir ..plzz use a light background...

[@VndNvwYvvSvv]

Nooo, dark is much easier on the eyes, especially for those who study after class, after work, etc.

[@gohanwanabe]

Shouldn't all possible outcomes be 16?

[@mtshibingu]

is it not 112 (8*7*2), if you divided the 3! with the 6 of the 8! thus the rest of the question is 112/256= 43.75?

[@jobanpreetmasko]

Watching after 12 years

[@BlazeMrdr]

couldnt one of those 3 flips be tails? like i understand the formula but doesnt that just give u the number of ways can arrange 3 flips out of a total of 8? doesnt that 56 include any tails?

[@HDSQ]

But its 240p

[@sunilupadhyay6225]

But it is shot in 2008

[@zsomborczoma]

The seven dwarfs became the eight flips! If you don't get the joke, you didn't watch the video, or you didn't pay attention!

[@bigboy321321321]

wat grade level is this for?

[@VndNvwYvvSvv]

Anywhere after 5th/6th I"d imagine. But you might do this even at a community college or intro to statistics.

[@dbapple]

Please someone can explain it to me? i cannot understand

[@bogdandospinescu12]

There is sth wrong to the demonstration. If we the same formula to find out for example the probability of getting 4 heads in 8 flips, than we have 27%, and is clearly that the probability should be 50%

[@gohanwanabe]

Why did he do 2^8 instead of 2*8?

[@zoolander0700]

With general notation, 2^8 is 2 to the power of 8 where 2*8 is 2 multiplied by 8

[@gohanwanabe]

Yes but if you flip a coin 8 times you going to get heads or tails, correct? So that means 2*8 not 2^8

[@zoolander0700]

gohan wanabe yes but we are interested in the possible combinations not just one set. An example you can do yourself is writing the possible combinations of 3 tosses, it isn't 2x3 (6) but 2^3 (8)

[@shazaduh]

"I am the god of probability" hahaha...

[@squidyplays859]

This comment was 10 years ago, mine will be too one day

[@sameenaz2006]

I like turtles !

[@wolfnorth7075]

His numeric calculation is wrong. he presented 8 flips, then he did a 8C3=56, that is wrong, his definition of numerator is 3 Heads out of the 8 flips. But the 8C3 is just pick the 3 flip results (Head or Tail) from the 8 flips.

[@bhz10]

this... confused.... the FUCK.... out of me.

[@spiderjump]

there are 56 combinations in which you get 3 H out of 8 flips. HHHTTTTT THHHTTTT TTHHHTTT and so on... therefore the prob of getting exactly 3 heads out of 8 = (0.5)^8×56

[@tricky92x]

I think I understand it this way better.

[@Serenityindailylife]

How many cars flipped after being high on special K? After the people died, you were found picking their seats... gross

[@kramerknipe4332]

I dont know why you didn't just use the nCr function that you would use on a calculator in school.

[@VndNvwYvvSvv]

Because you need to understand how a concept works before you just go punching keys, especially when you later have to combine expressions. You have to know what they really mean and how they affect each other.

[@Foamy_Bubbles]

e

[@tdinh08]

no bud, pay attention lol , exactly 4 head is 27%, it would be 50% if u add 4 head or less, meaning 4 heads, 3 heads, 2 heads, 1 head.

[@christineren109]

any armys here?!????????XD

[@Bot-tm7hs]

It took so long to find that one combination. Just use a calculator for that part irl

[@ifechukwujohnpaulumeh3740]

I didn’t understand a thing

[@NiftyFingers]

This is a pretty good channel. Keep it up man!