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The Hardy-Weinberg Principle: Watch your Ps and Qs

  Рет қаралды 586,073

ThePenguinProf

ThePenguinProf

Күн бұрын

The Hardy-Weinberg Principle states that allele and genotype frequencies in populations remain stable over time, given certain assumptions. What assumptions? What does the principle mean? And how do you SOLVE those Hardy-Weinberg PROBLEMS? Everything shall be revealed in this video - with some penguins of course. They make everything go down easier.
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Links to Videos Mentioned:
Mendelian Genetics: • Mendelian Genetics - F...
How to Solve Genetics Problems: • Solving Genetics Problems
Solution for the additional problem I showed at the end:
Allele Frequencies:
q = 0.04
p = 0.96
Genotype Frequencies:
homozygous dominant: 0.92
Heterozygous: 0.08
Homozygous recessive: 0.002
Answer to the additional problem step-by-step: www.penguinprof.com/uploads/8/...
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Video Details:
Population Genetics:
The Hardy-Weinberg Principle
You need to know:
gene vs. allele
gentoype vs. phenotype
understanding probabilities (and vs. or)
Punnett Square
Hardy-Weinberg Principle
Timeline of Discoveries
Darwin, Mendel, DeVries, Correns
Hardy, Weinberg, Castle
Mendelian Genetics Gets HOT
Particles are inherited!
Traits aren't blended!
Cambridge opens a department of Genetics
So What's it All About?
It's about frequencies
When talking about population genetics, we are interested in the prevalence of a particular allele or genotype in a population
The Hardy-Weinberg Principle States:
Frequencies of alleles and genotypes in a population will remain constant over time in the absence of other evolutionary influences
Assumptions
Organisms are diploid
Generations are non-overlapping
Population must be large
No immigration or emigration
No mutation in the gene of interest
No natural selection occurs (individuals reproduce at equal rates)
Mating is random
Alleles and Allele Frequency
Penguin Prof Helpful Hints
The Sum of All Possible Outcomes MUST Equal 1
p+q = 1
ALLELE FREQUENCY
2 Alleles = Genotype
p2 + 2pq + p2 = 1
What if There are Three Alleles?
(p, q and r)
Sample Problem
In a population of 1,000 penguins, 12 have blue feet. Find the frequency of the blue allele, the yellow allele and the frequencies of the three possible genotypes in this population.
Solving Hardy-Weinberg Problems
Assign the alleles
Frequency of the dominant allele is 'p'
Frequency of the recessive allele is 'q'
Calculate q by taking the square root of the number of homozygous recessive individuals
Calculate p (the allele frequencies must equal 1, so p = 1 − q)
Use p and q to calculate the other genotype frequencies:
frequency of homozygous dominant individuals = p2
frequency of heterozygous individuals = 2pq
frequency of homozygous recessives = q2
This may help:
Hardy-Weinberg Punnett Square
Try Another One...
In a population of 130,000 magical mice, green fur is dominant over orange. If there are 300 orange mice in a population of 130,000, find the following (assume population is in Hardy-Weinberg equilibrium):
1. Frequency of dominant (green) allele
2. Frequency of recessive (orange) allele
3. Frequency of each genotype

Пікірлер: 412
@erinrobison2547
@erinrobison2547 8 жыл бұрын
Okay seriously?! This took my professor an entire hour to explain, and I still walked away confused. And here I am, six minutes into your video and I've already got it. THANK YOU SOOOOO MUCH
@Penguinprof
@Penguinprof 8 жыл бұрын
Love to hear it! Thanks for watching!
@davidfrisch5099
@davidfrisch5099 8 жыл бұрын
True story...
@user-ci8sg4mz5k
@user-ci8sg4mz5k 7 ай бұрын
Love the way you explained it. Thank you 😊
@auchandrive3710
@auchandrive3710 2 ай бұрын
Et ce ratio il l’a bien compris ce principe ?
@samanthabridges2108
@samanthabridges2108 8 жыл бұрын
I hope this reaches you because your videos have saved me. It took 12 minutes to understand something I've been struggling with for a week now. You're the greatest and I am going to be a frequent visitor cause your videos are going to help me rock this semester! Thank you so much for all your time and efforts!
@Penguinprof
@Penguinprof 8 жыл бұрын
+Samantha Bridges I'm so glad you are finding them helpful - you are SO welcome! Now go KILL those midterms!!! PENGUIN POWER!!!!
@tieler151
@tieler151 8 жыл бұрын
+ThePenguinProf how do you convert a frequency into population
@totallymcmylastname9077
@totallymcmylastname9077 8 жыл бұрын
With proportions. The same stuff you do with stochiochemistry or mathematics. but you'll need to know the numbers of the guys you're interested in first ex. there are 13 brown rats out of 41 so its [13/41] so if you're asked for numbers of brown rats in a den of 1000 rats you just need to set up [13/41] = [x/1000] since frequency = specimens/total population. You can just set up the ratios for that.
@harmabebae5500
@harmabebae5500 7 жыл бұрын
Samantha Bridges iikk
@nguyenvietnhan4605
@nguyenvietnhan4605 2 жыл бұрын
oooo
@canadianslumbaparty
@canadianslumbaparty 7 жыл бұрын
Can I just say, this is awesome. I'm a third year biology major and having material explained like this is the actual best thing ever. Everything is going to be okay now that I know about penguin feet.
@Penguinprof
@Penguinprof 4 жыл бұрын
So glad to hear that! Yes, if you know about the feet, you'll be just fine.
@gabino3649
@gabino3649 4 жыл бұрын
I'm gonna need gor you to help out in some things if it's possible then
@heatherstone333
@heatherstone333 8 жыл бұрын
I'm a 28 year old married woman with two dogs who enjoys peace and quiet and cups of tea. I decided I wanted more in life so I gave up everything and worked my ass off so I could get into University. I'm now preparing for my last summer exam of my first year at Uni, which is Genetics, tomorrow. I was just sat here crying over my lecture notes totally not understanding a thing and feeling like a total failure. If I don't pass then I disappoint everyone who believed in me and prove all those that didn't right, and will have got myself into thousands of pounds of debt for nothing. This video has just saved my life. I was about to give up altogether, but this video WORKED. I wish I could hug whomever made this video because I'm crying for a whole different reason now! I even got the question at the end right on my own!!! 12 minutes 15 seconds - this video literally may have changed the outcome of my life, I'm totally serious. Thankyou from the bottom of my heart, if only my University lecturers put things as simply as you have.
@Penguinprof
@Penguinprof 8 жыл бұрын
I can feel your hug from here!!! YOU made my day!!! I am so happy you didn't give up and I hope this feeling will keep you going... you can do this and now you know there's a little penguin on your shoulder who will nip at you when you think you can't do it. Congratulations to you and thank you for letting me know I could help.
@reikalake1456
@reikalake1456 8 жыл бұрын
You're the best! I read this in my Bio book and they worded it so poorly that I was confused in no time. You have such a nice/articulate speaking voice, clear method of teaching, and a great sense of humor. It cleared everything up in no time!
@mzblue
@mzblue 6 жыл бұрын
God bless you... just wanted you to know that 5 years later, someone still find this helpful.
@paulmatei9049
@paulmatei9049 4 жыл бұрын
This video literally just saved me...here I am on youtube browsing through hundreds of videos and when I finally got here it was like I found a secret treasure. Thank yooouuuuu!!!! Please dont stop making videos, they are so helpful and you are so nice. Its impossible not to understand when you make it look so easy.
@Penguinprof
@Penguinprof 4 жыл бұрын
So kind of you to say - I'm SO glad it was helpful!!!
@PatchJeffa
@PatchJeffa 9 жыл бұрын
That was a better explanation than any I've had at uni so far
@jenniferwang946
@jenniferwang946 3 жыл бұрын
I honestly really love how this video is so useful to people of all ages and types! Thanks for making it!
@Penguinprof
@Penguinprof 3 жыл бұрын
You're so welcome!
@spiffysixxsense2694
@spiffysixxsense2694 8 жыл бұрын
when i got the mice question at the end right all by myself, i almost cried....
@nyevs21
@nyevs21 8 жыл бұрын
+SpiffySixxSense how did you got it? omg help huhu
@billytragyu4679
@billytragyu4679 8 жыл бұрын
+Raiza Marie Nieves just stop being such an idiot. That is the solution. :)
@priangelrae9738
@priangelrae9738 8 жыл бұрын
+Billy Tragyu no need to be rude wtf
@rachelduncan2406
@rachelduncan2406 6 жыл бұрын
i just laughed so hard
@shriyasrivaz3369
@shriyasrivaz3369 5 жыл бұрын
@@nyevs21 so question says that - phenotype =orange recessive mice are 300 Phenotype =2 alleles =q×q(recessive pheno) Or p×p(domint pheno) So orange mice out of total =300/130000 = 0.0025= q×q Recesv allele? = q = sqroot(0.0025)=0.0479 Dominant allele? =p We know, tot allele =1 therefore p=1-q =0.0.952
@TheMarleneshow
@TheMarleneshow 7 жыл бұрын
I've sat in class for two hours and watched probably four videos, and you have explained it so well to me. Thanks a lot! Hoping to ace any hardy-weinberg problems on my test tomorrow because of you :)
@MegaDara999
@MegaDara999 6 жыл бұрын
This is honestly such a clear example. I was watching some other video before and wast getting it. Thank you so much.
@lovelystar2849
@lovelystar2849 7 жыл бұрын
She said by the end of this video you will understand it! and I was like yeah right. End of the video I'm doing problems in my head 😂😂 ty soo much!!!!!
@Penguinprof
@Penguinprof 4 жыл бұрын
You are SO welcome!!!
@AquaticLogic
@AquaticLogic 7 жыл бұрын
This video is so well done. Thank you! I'm in a 4th year genetics class and i'm so thankful you posted this!
@shiilovesdogs
@shiilovesdogs 10 жыл бұрын
Wow this really helped me for my ecology class, and the other genetics videos helped me a lot for my genetics class. So clear, understandable and fun! I wish I was your student in your class!! Penguins are cute and It's nice how your passion for them allowed you to work with them!! I read your story on your site, and it was really touching. It motivates me to follow my dreams and never give up!! Thank you so much again and I look forward to more biology videos!! :) God Bless.
@thedevilthatyouforgot7981
@thedevilthatyouforgot7981 4 ай бұрын
THANK YOUUU I'VE BEEN SEARCHING VIDEOS ABOUT THIS HARDY WEINBERG STUFF AND THIS IS THE ONLY ONE I CLEARLY UNDERSTAND
@Penguinprof
@Penguinprof 4 ай бұрын
I AM SO HAPPY IT WAS HELPFUL!!!!!!
@TankuBOSS
@TankuBOSS 4 жыл бұрын
I wish my professor would make problems the way you make them. She puts them into like 10 different steps that are not even in colloquial terms and I just can't wrap my head around it. You're really good at what you do!
@Penguinprof
@Penguinprof 4 жыл бұрын
Thank you so much!
@sanatdas2011
@sanatdas2011 6 жыл бұрын
This is really helpful & I really appreciate the amount of effort that you had to put. Thanks, @ThePenguinProf.
@dalia9512
@dalia9512 6 ай бұрын
You're literally the sweetest most passionate teacher I've ever come across. 😭 I teared up watching this! You made it sound so fun! ❤God bless your kind soul!
@Penguinprof
@Penguinprof 6 ай бұрын
Wow, thank you!
@KaseyJBieber
@KaseyJBieber 6 жыл бұрын
You have saved me from failing my final, you a heaven sent!!! Thank you !
@IamGianneisy
@IamGianneisy 2 жыл бұрын
I have been struggling for 2 weeks in my lab class and my lecture, asking TA's on how to not over think these problems and your video is the one to teach and simplify it for me! Ugh seriously amazing!
@Penguinprof
@Penguinprof 2 жыл бұрын
I'm SO glad it was helpful!
@adriennesmith3601
@adriennesmith3601 7 жыл бұрын
Thank you so much!!!!!! I have a major exam on this tomorrow and we just learned it today. You saved me!!!
@wade5941
@wade5941 4 жыл бұрын
Thank you for all you do to provide information in a clear and unbiased manner. You make the complicated understandable.
@Penguinprof
@Penguinprof 4 жыл бұрын
Thank you SO MUCH!!! :)
@tomsadeh9624
@tomsadeh9624 7 жыл бұрын
Best genetic timeline I've heard! Great explanation and easy to follow :)
@pratitibanerjee7621
@pratitibanerjee7621 7 жыл бұрын
I study in high school in India and we have this in our syllabus. Needless to say our teachers do a lousy job of explaining it... and who ends up feeling stupid ? US. Thanks for making me feel not-so-stupid again. Keep up the awesome work.
@Penguinprof
@Penguinprof 7 жыл бұрын
Thank you for watching and for sharing this VERY important message... you should NEVER be made to feel stupid!!! No one is born with knowledge about how to solve these problems (or how to do differential equations or how to dance a Waltz or anything else for that matter) but we all have the potential to learn these things - and it is essential, in my opinion, that we have safe, encouraging learning environments in which to explore, to question and to be wrong. If I can create that kind of environment through these videos, well, that is my career goal. And I thank you from the bottom of my penguin heart for letting me know that you understand what I am trying to do. Best of luck to you in your studies - keep in touch!!!
@pratitibanerjee7621
@pratitibanerjee7621 7 жыл бұрын
This just made my day !!! And yes you couldn't be truer about the fact that we need to get it wrong to get it right eventually. Contrary to popular belief, biology isn't ALL about cramming up names mindlessly and when teachers like you show us the elegant logic behind it all....there could be nothing better !!! Thank you so much.
@pinkubhadoria6469
@pinkubhadoria6469 5 жыл бұрын
@@pratitibanerjee7621 Hardy weinberg principle is in class 12th cbse
@saveUyghurs
@saveUyghurs 11 жыл бұрын
You speak in such a reassuring way, you're like my fairy godmother, I love it! Other teachers make you (me at least) feel incapable of learning anything. And all of your cute little graphics are awesome :)
@Penguinprof
@Penguinprof 4 жыл бұрын
Awww... thank you so much!
@lizbethvalle8911
@lizbethvalle8911 8 жыл бұрын
This was super helpful, I love the way you explained it, and the step by step examples really helped a lot :D
@aaronneiman2139
@aaronneiman2139 9 жыл бұрын
Needed this for my thesis! Thank you so much!
@Nazmussakib1548
@Nazmussakib1548 Жыл бұрын
I am so glad that I have found this video. It is mind blowing how the concept is explained here so easily. Appreciate the work.
@Penguinprof
@Penguinprof Жыл бұрын
Glad it was helpful!
@lorityler6398
@lorityler6398 7 жыл бұрын
Thanks so much! Your videos have really helped me get caught up! Plus the penguins are super adorable!
@anamartinez4002
@anamartinez4002 10 жыл бұрын
This is the best video on Hardy-Weinburg that I have seen so far. Extremely helpful !!! Thank you so much !
@boccaluppo930
@boccaluppo930 7 жыл бұрын
The key is to do this problem over and over, and over. I am finally getting it!
@1990SammieJ
@1990SammieJ 6 жыл бұрын
I made a few pages of notes using this video, it was very helpful.
@zullyhall3438
@zullyhall3438 6 ай бұрын
What an amazing channel! I enjoy watching random knowledgeable videos and this takes the entire cake (I watched the donuts video hehe and loved it). Very well explained videos. Kuddos (clapping). Wish all my previous professors had your style of explanation (on any subject matter). Makes paying attention worth the time. Kept me from snoring past the first sentence. Ty.
@Penguinprof
@Penguinprof 6 ай бұрын
Thank you so much for watching and for sharing such kind words!!!
@floppyfox6930
@floppyfox6930 9 жыл бұрын
Really easy to understand. Like your style and your bright voice .Keep on uploading videos ! :D
@amberbosma7464
@amberbosma7464 5 жыл бұрын
I have a biology test tomorrow, and I did not understand a thing about this but I could not find any good Dutch videos (I am from the Netherlands) so I started searching for English videos and this helped me so so much! thank you!:)
@lukeisunlucky
@lukeisunlucky 5 ай бұрын
Holy honk lady i love you! My professor spent 3-4 hours on this and still didn’t understand a thing! Thank you!
@Penguinprof
@Penguinprof 5 ай бұрын
Well, I love you too!!! I'm so glad it was helpful!
@984594386937468374
@984594386937468374 11 жыл бұрын
I was sick for a few days and missed what my students are calling the "hardest unit to date" but this video was SO CLEAR! Thank you for the help!
@windygoga5698
@windygoga5698 2 жыл бұрын
LET LENI LEAD!!!
@TheElusiveDirector
@TheElusiveDirector 9 жыл бұрын
Thank you so much for creating this! You made it so easy to understand!
@outlander271
@outlander271 3 жыл бұрын
Excellent graphics and excellent narration! Subbed!
@Penguinprof
@Penguinprof 3 жыл бұрын
Thank you! Welcome to the colony!!!
@harshavenkatesh898
@harshavenkatesh898 7 жыл бұрын
Thank you so much! You explain it so well! Really helped me with my test
@kdesignkhalifa
@kdesignkhalifa 5 жыл бұрын
Thank you! I finally get it! You're a great teacher
@jacquicl1984
@jacquicl1984 10 жыл бұрын
you're an excellent professor! Thank you so much for your help ;P
@karlatrujillolcegsolana3702
@karlatrujillolcegsolana3702 3 жыл бұрын
Dear Person that decided to share this knowledge. You are Aaaamazing! Thank you for walking us through this concepts. It is not difficult to understand, but it needs to be broken down and you did that in such an awesome way.
@Penguinprof
@Penguinprof 3 жыл бұрын
Glad it was helpful! Thanks for watching and for your lovely comment.
@eviegraham6094
@eviegraham6094 6 жыл бұрын
you are literally the best!! I have been learning this for 2 years and now I get it!!!!!!!
@MsNinjani
@MsNinjani 11 жыл бұрын
very helpful!!! you explain things so plainly and clearly. thank you so much
@TheGlamorization
@TheGlamorization 7 жыл бұрын
wow, I don't think you understand how grateful i am for this! thank you thank you thank you!!!!!!!!!!!
@graceb2404
@graceb2404 9 жыл бұрын
Excellent video! Just have to remember that after assigning p and q alleles, I have to square root the homozygous recessive genotypes to get q. After obtaining q, everything is golden.
@ETFbvbAA
@ETFbvbAA 7 жыл бұрын
OMG I ACTUALLY GOT THE RIGHT ANSWER WHEN I DID THE PROBLEM AT THE END THANK YOU SO MUCH I HAVE A MIDTERM TOMORROW AND MY TEACHER JUST WENT OVER THIS IN LIKE 3 MINUTES THANK YOU THANK YOU THANK YOU
@Zeke347
@Zeke347 3 жыл бұрын
Thank you so much! I didn’t understand any of this until your video!
@Penguinprof
@Penguinprof 3 жыл бұрын
You're welcome! I'm so glad it was helpful!
@RecendezM008
@RecendezM008 10 жыл бұрын
Much appreciation!! Gotta quiz tomorrow, so this helped a lot. Thank you !
@keilacobham4894
@keilacobham4894 5 жыл бұрын
Thank you so so so so much for this fascinating explanation, I have been trying to figure this out for a long time and I couldn't find anyone that could make it clearer for me, even though I am pretty good in math, I needed to know how and why of the steps taken to solve. Two of my BIO tried to explained but I wasn't clear, but you have made it so easy and simple. Thanks again, I will definitely ace this part on my exam now. Thanks, much appreciated
@binujpin
@binujpin 5 жыл бұрын
So clearly explained ; great teacher !
@misstaniamaryam
@misstaniamaryam 3 жыл бұрын
BRILLIANT, you took such a difficult topic --> Made it soo simple and easy to understand. THANKS A LOT!
@Penguinprof
@Penguinprof 3 жыл бұрын
Glad it was helpful!
@devikrishna9118
@devikrishna9118 6 жыл бұрын
Thank you soo much. I totally understood this now..my teach took hours explaining this..
@courtneymaynard8853
@courtneymaynard8853 3 жыл бұрын
I have a BIO final tomorrow and I was dreading the Hardy-Weinberg questions... NOT ANYMORE! This video was extremely helpful, thank you!
@Penguinprof
@Penguinprof 3 жыл бұрын
Glad it helped!
@premkumarjulien
@premkumarjulien 9 жыл бұрын
Beautifully presented and Inspirational. I am also a teacher.
@leilamitchell3489
@leilamitchell3489 5 жыл бұрын
OMG I love you! It took only 12 minutes to understand something I've been struggling with for a week
@grichardgarrett1970
@grichardgarrett1970 4 жыл бұрын
Leïla Mitchell Hello
@grichardgarrett1970
@grichardgarrett1970 4 жыл бұрын
Leïla Mitchell well I am a genius
@simplybella9671
@simplybella9671 9 жыл бұрын
Bless your heart! I have spent almost my entire day trying to study this and you explained in less than 13 minutes everything so clearly with such perfection Thank you!!!!!! 😭
@grichardgarrett1970
@grichardgarrett1970 4 жыл бұрын
SimplyBella
@TheBoombreaker
@TheBoombreaker 3 жыл бұрын
I liked your video better, than any other in my mothertongue. You did a good job :)
@Penguinprof
@Penguinprof 3 жыл бұрын
Wow, thanks!
@quiquev9214
@quiquev9214 10 жыл бұрын
Keep on the good work! Thank you.
@pukamon1681
@pukamon1681 9 жыл бұрын
Thank you so much! Now I totally get it.
@barbarabm94
@barbarabm94 9 жыл бұрын
Thank you so much! You just made it so easy to understand
@thrashers8041
@thrashers8041 11 жыл бұрын
Only video that helped me gain a full understanding of the principle. Thanks!
@Kindatheist666
@Kindatheist666 4 жыл бұрын
Wow!!! Absolutely fabulous!!! Thanks and leave it here please!!!
@Penguinprof
@Penguinprof 4 жыл бұрын
You got it! Thanks for watching!
@oliviaw5250
@oliviaw5250 6 жыл бұрын
This was an excellent video!!
@barbaradixon3820
@barbaradixon3820 9 жыл бұрын
I can't imagine why this video received 13 thumbs down :^( Could it be they are unhappy no likes their videos on the same topic? This is an excellent video. You taught me in minutes what my professor with a Doctorates degree couldn't. Thank you.
@Remascard
@Remascard 9 жыл бұрын
While the content past four minutes was incredibly useful for biology students wanting to solve hardy-Weinberg problems, the first four minutes contain history which is not necessarily applicable to H-W problems, and the individuals who down-voted may have felt that ThePenguinProf wasted 4 minutes unnecessarily.
@isaachernandez7178
@isaachernandez7178 6 жыл бұрын
the dislikes come from proffesors at universities who do their job worse than this woman does and get mad ;))) fucking greatest explanation of all time thank u
@SarahGuadagnin
@SarahGuadagnin 8 жыл бұрын
THANK YOU!!!! I have an exam on this today, helped a ton!!
@Doctorrenee123
@Doctorrenee123 4 жыл бұрын
WOW WHAT A GREAT VIDEO! SO CLEAR AND HELPFUL! When i got the correct answer for the practice Magical mice problem, i was extremely proud of myself! THANK YOU FOR THIS!! GOOD HELP
@deepaksoner4034
@deepaksoner4034 4 жыл бұрын
Brilliantly explained...thank you so much
@calypsozachary3929
@calypsozachary3929 5 жыл бұрын
makes so much more sense! thanks
@rurusiddi
@rurusiddi 7 жыл бұрын
you explained it better than all the men on youtube thank you! their voice was so monotone and not clear enough
@raykangoo4674
@raykangoo4674 9 жыл бұрын
thanks a million i finally understand this after soo many times of trying
@jessicapeltier9205
@jessicapeltier9205 4 жыл бұрын
Thank you so much for the clarity. If it wasn't for the way you went over the steps of the actual formula and the square root part I would have been still beating my head into the ground last night.
@arielhemingway8899
@arielhemingway8899 7 жыл бұрын
I finally understand!!! Thank you so much! I love your teaching style and wish my teacher was like you.
@ComfyLaur
@ComfyLaur 3 жыл бұрын
This video was explained so well and actually helped me to understand better. THANK YOU!!!!!!
@Penguinprof
@Penguinprof 3 жыл бұрын
You are most welcome! I'm so glad you found it helpful.
@jabeenthaz133
@jabeenthaz133 8 жыл бұрын
Amazing explanation. Thank you so much for this video
@Penguinprof
@Penguinprof 8 жыл бұрын
+Jabeen Thaz You are so welcome!!
@richb3014
@richb3014 Жыл бұрын
Very well explained. You can also check if you have calculated the frequencies correctly (10:58) in the table, because the total should also = 1 (0.79+0.2+0.01 =1).
@Penguinprof
@Penguinprof 11 ай бұрын
Yes, thank you!
@Jasmijnwh
@Jasmijnwh 8 жыл бұрын
This was so good! Thank you! I'm from the Netherlands but I understood this better than Dutch explanations :)
@deepaksoner4034
@deepaksoner4034 5 жыл бұрын
Really easy one... excellent job..
@TheYardvark
@TheYardvark 9 жыл бұрын
Excellent video, really helped me a lot!
@mayaarciva2097
@mayaarciva2097 3 жыл бұрын
I don’t know if you are going to see this ,but thank you so much you helped me understand it much better :)
@Penguinprof
@Penguinprof 3 жыл бұрын
I see you and I am so glad it helped!
@kiranpunjani3853
@kiranpunjani3853 10 жыл бұрын
I love this video...simple and to the point
@markbinnis6210
@markbinnis6210 5 жыл бұрын
Excellent video.
@saimp7170
@saimp7170 7 жыл бұрын
Thank you mam this was really helpful to me , you are amazing and little fun you do in the videos is just awesome
@josephcjose1366
@josephcjose1366 5 жыл бұрын
Very helpful. Thank you
@tellau
@tellau 4 ай бұрын
Omg thank you so much i have an exam tomorrow and i lost my mind finding the difference between p and p² stuff but now it all makes sense 😭💗
@Penguinprof
@Penguinprof 4 ай бұрын
You got this! Glad I could help!!!
@barcafun100
@barcafun100 10 жыл бұрын
thanks for the video! it makes it very clear! didnt really get it in lecture but i do now thanks to the video!
@bobrcnal
@bobrcnal 9 жыл бұрын
Thank you. You're my angel this will help a lot!
@Lisa-qt4hh
@Lisa-qt4hh 10 жыл бұрын
This video was really clear and helpfull, thank you so much !! ☺🐧
@digiconvalley
@digiconvalley 11 жыл бұрын
I love your style! Thank you very much!
@parisa5670
@parisa5670 5 жыл бұрын
Oh man i love you. Thank you so much !!
@katiedevine5479
@katiedevine5479 8 жыл бұрын
Thank you so much i have a zoology exam today and i was really struggling with this, now i understand its easier than i thought x
@Penguinprof
@Penguinprof 8 жыл бұрын
+Katie Devine Excellent! Hope you did well!!!
@sakthivelb9074
@sakthivelb9074 3 жыл бұрын
Quality content. Keep it up
@Penguinprof
@Penguinprof 3 жыл бұрын
Thanks, will do!
@light-fd4vt
@light-fd4vt 6 жыл бұрын
Thank you so much😁😊😆❤ u explained it really well
@kariopichka4061
@kariopichka4061 9 жыл бұрын
Great vide, extremely helpful, THANKS so much!!!!
@praveenkumartripathi8266
@praveenkumartripathi8266 5 жыл бұрын
Explained very nicely!
@muskandalal5585
@muskandalal5585 4 жыл бұрын
Really very helpful..thank you
@toobawaheed6091
@toobawaheed6091 9 жыл бұрын
Wonderful tutorial, truly amazing and helpful thankyou so much..........
@jessicapreece5265
@jessicapreece5265 9 жыл бұрын
Yessss!!! I can do it now :) Thank you penguins :D
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