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Biology: Laws of Probability: Multiplication Rule


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About this Lesson

  • Type: Video Tutorial
  • Length: 10:49
  • Media: Video/mp4
  • Use: Watch Online & Download
  • Access Period: Unrestricted
  • Download: MP4 (iPod compatible)
  • Size: 115 MB
  • Posted: 07/01/2009

This lesson is part of the following series:

Biology Course (390 lessons, $198.00)
Biology: Mendelian Genetics and Mutation (36 lessons, $54.45)
Biology: Laws of Probability (4 lessons, $8.91)

Taught by Professor George Wolfe, this lesson was selected from a broader, comprehensive course, Biology. This course and others are available from Thinkwell, Inc. The full course can be found at The full course covers evolution, ecology, inorganic and organic chemistry, cell biology, respiration, molecular genetics, photosynthesis, biotechnology, cell reproduction, Mendelian genetics and mutation, population genetics and mutation, animal systems and homeostasis, evolution of life on earth, and plant systems and homeostasis.

George Wolfe brings 30+ years of teaching and curriculum writing experience to Thinkwell Biology. His teaching career started in Zaire, Africa where he taught Biology, Chemistry, Political Economics, and Physical Education in the Peace Corps. Since then, he's taught in the Western NY region, spending the last 20 years in the Rochester City School District where he is the Director of the Loudoun Academy of Science. Besides his teaching career, Mr. Wolfe has also been an Emmy-winning television host, fielding live questions for the PBS/WXXI production of Homework Hotline as well as writing and performing in "Football Physics" segments for the Buffalo Bills and the Discover Channel. His contributions to education have been extensive, serving on multiple advisory boards including the Cornell Institute of Physics Teachers, the Cornell Institute of Biology Teachers and the Harvard-Smithsonian Center for Astrophysics SportSmarts curriculum project. He has authored several publications including "The Nasonia Project", a lab series built around the genetics and behaviors of a parasitic wasp. He has received numerous awards throughout his teaching career including the NSTA Presidential Excellence Award, The National Association of Biology Teachers Outstanding Biology Teacher Award for New York State, The Shell Award for Outstanding Science Educator, and was recently inducted in the National Teaching Hall of Fame.

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Perhaps it's time to graduate from Punnett squares and start looking at some mathematical ways we can do and predict some of these crosses. You know, I just used a very important word and I want you to understand this word predict. The thing that gets most students when we start talking about this idea of Mendelian genetics, is they think it's certainty. But it's not, it's probability and sometimes I almost like to feel like it's possibility. So, when we come down to it we have to be talking about, well what is it that we're doing when we say, "Oh, let's do a Punnett square." We're looking at the probable genotypes using the laws of chance.
Take this coin, for example, on one side I have a S and on the other side I have a s. Now, when I flip the coin and it lands square right there in the middle of the table, it comes up to be a S. So therefore, what's the possibility or probability that the next time around it's going go be a s. The answer is, the same as it was this time. But could I get a S again? Yes, I can. I could get a S again. See, each time I flip this coin, I could get a S or s. This time and I got a s. It's the laws of chance. Guess what. Every time an organism flips meiosis, it's the laws of chance. Overtime an organism produces a sperm, it's the laws of chance. Every time an organism makes an egg, it's the laws of chance.
Which gamete are you going to get? Now, that means if I say to you, "Okay, I got a S, all my offspring are going to be S." No, that's not true, but you've got to be careful of this. You have to realize we're talking probabilities, laws of chance. We'll come back to these guys in a second. Let's talk about the laws of chance. Let me ask you a question. Here's two parents, we're going to cross them. We'll make this one the male and this one the female. They are both heterozygous. What are the odds that I am going to get a SS from this? Well, thinking of Mendelian genetics. If you do Punnett squares, you know--what's he doing. We get a Ss cross at the Ss and you do your Punnett squares and you know there's a one out of four chance of getting a SS. Okay?
I did. I got it. You see. Do you know what the odds are of that happening? One out of four. The point here is this. That I got the SS, but there's a mathematical way we can do this. Watch. Let's take it one at a time. What are the odds that the sperm that this mail produces will have S? You know that the odds of him producing a sperm with S are one out of two. What are the odds that she will produce an egg with a S? One out of two. So, when we cross them we could see, one out of two, one out of two and multiplying them together we get one out of four. Now you probably intuited that. That's intuition and very often probability is intuition. But if you were able to intuit that, you just made up a law. We call it the multiplicative law of probability.
The multiplicative law is basically this. What the multiplicative law says is this, that the probability of two independent events--the probability of two independent event. Let's talk about that for a second. I hate to interrupt in the middle of a thought, but independent events--this is independent of this. That male didn't care what egg that female made. Two independent events both occurring is what? Is the product of their individual probabilities. Get it? The product of their independent probabilities. I really want you to understand and not memorize here. Understand this principle and you'll see that there's like a lot of different places in genetics we can use it.
Let me give you an example. From this same cross, can you compute the odds of getting a ss? It's an easy one. Well, let's take a look. We know that we have a Ss, and a Ss. Right? We know that if we do--I'm showing you the long way first. So, we have a given known here. You know what I'm going to do later. I mean, I can give you two, three, four traits. You're not going to want to be drawing Punnett squares for those, trust me. But you know if you draw Punnett square, you know that it's a one in four chance of getting a ss from your Punnett square. Well, let's just do the math.
What are the odds of getting a s gamete from this. To get a ss, here's what we have to ask. What are the odds of getting a s sperm from him? One out of two, because in order to get a ss f[1], we have to have a s from dad and a s from mom. What are the odds of getting a s from mom? One out of two. One out of two times one out of two, one out of four. Okay, I'm going to give you a hard one to try. I do the easy ones, you do the hard ones. Ready? Here we go. I'm going to give you this to try, we're going to stop, you're going to try. You're going to give me an answer and we're going to see if you get it right. This one is going to be a little bit trickier.
I'm going to talk about a human disease called achondroplasia or achondroplastic dwarfism. I'll tell you a little bit about this disease. It's a dominant gene. The disease, the disorder is a dominant gene. So, we're going to say that D equals achondroplasia. d is normal height. Let me give you another one. DD is lethal, the fetus never survives. Okay? You can get the idea I'm tricky. Here's my question. What are the odds of two people afflicted with achondroplasia, two achondroplastic dwarfs, having a normal child. Use statistics don't do a Punnett square. What are the odds of them having a non-achondroplastic child? You work on that right now.
Got an answer didn't you. Let's take a look. Now here's the trick. Remember what I told you. This whole idea of DD is lethal. So, here's the thing, these two people--I said that to you because I wanted you to understand that neither of these two people could be DD. You know their genotypes. Their genotypes are Dd crossed with Dd. Now, here's the trick is this. If you--this was a nasty question to give you, but you know that's where teacher go. What we're asking is, we want to do this. We know that there's a dd to get the child.
Here's the key. If the d comes from dad, well what's the odds that he's going to get a d from dad? One out of two. What are the odds that he's going to get a d from mom? One out of two. Here, I'm about to teach you a lesson. Not like a lesson like you've been naughty children, but sometimes we have to think through our genetics and be careful. At first glance, it says here that the answer should be one out of four and I accept that as a correct answer, but you've got to be careful. Look at the way I phrased the question. I said to you, "What are the odds of their having an achondroplastic child?" Now what did I say to you before? I said the fetus never develops. So, if they have a child, is there the faintest possibility that it's DD? The answer is no. So, if I had said to you, "What are the odds that they're going to have a normal child?" What are the odds that they're going to have a normal conception, sperm and egg, the odds are one out of four.
I'll take that, but what are the odds that that child that is delivered is normal, will be normal? Well the odds there are one out of three. In this case, the statistics will mislead us. So, they always have to--I did this to you on purpose. You always have to know your genetics before you do your statistics. Because the key is, it's one out of four to have a conception, dd, but you know that those children will be either or we know that the possible combinations of DD, Dd, dd, we know that the child can't be that. So, it's really one out of three. So, I just bring you a word of caution. Statistics are good, but remember we're learning genetics.
Mendelian Genetics and Mutation
Laws of Probability
Laws of Probability: Rule of Multiplication Page [2 of 2]

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