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Genetics

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2. Mendel's Laws of Inheritance

Probability and Genetics

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Probability

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Hi in this video, we're gonna be talking about probability and genetics. So geneticists use probability and math all the time because they want to be able determine, you know, what's the chance or what's the probability that an offspring will have this phenotype or have facilities or have this mutation, any of these things. And so we have to be able to understand probability laws in order to understand those types of questions. You know, what's the chance that this will happen? So there's three. I want to talk about. The first is the product law and the product law is used when you have two independent events that are occurring together. So the example um that I'm gonna use is coin tosses because that's always using probability. But if you toss a penny and a nickel at the same time, what's the probability of both being heads? So if you toss a penny and a nickel, each has one half chair chance of being heads, correct? Right. The penny has a one half chance of being heads or tails. The nickel has a one half chance of being heads or tails. Each or independent. Each other of each other. Whatever the penny is has no effect on whatever the nickel is going to be and they're occurring at the same time, they're being tossed together. So what you do is you multiply them. So you take one half, multiplied by one half and that equals 1/4 or 25%. So that's when you use the product law, The second one is the some law. And this is of course adding because it's the sum and it occurs independent events occurring together. But you use it when the events could occur in more than one way. So the example of this is the same example tossing a penny and tossing a nickel. But what you want is you want one being heads and the other being tails. So there's two possible ways that could happen, right? The penny could be tails and the nickel could be heads or the penny could be heads and the nickel could be tails. Now each one of these has a 1/4 chance of happening. How do I know that? Because you have these two options? They could both be heads or they could both be tails. And there's no other combination of these things happening, right? And these would both be 1/4 as well. So in the some law to understand the probability of one being heads and the other being tails, you add them. So you take 1/4 plus 1/4 equals what? One half or 50%. And that's the some law. Now, the third one we're going to spend a little bit more time talking about because there's really two ways to go about doing this and this is the binomial theorem. And this is when there are alternative ways to achieve some type of combination of events. So the example that I'm gonna use is what is the probability that a family with four Children, two will be male and two will be female. There's four Children, two male, two female. What's the probability of that happening? So the first option is using this formula here, A plus B race to the end. So what are all these stand for? Well, A is the male probability which is one half. We know this because there's two out of four males and B is the female probability, which is also one half because it's two out of four. So we can put one half plus one half. But now we need to know what is, so n is actually determined by um this so there's four Children. So it is the number of possible outcomes. So here we have four. Now you can do this two ways. Now if you are good with math, you can just write it out and do the math and get the formula which you would input A and B for and then get the probability Or if you don't feel like doing this, you can use this cheap table. So what this is is you know that you're in is four. So here we have zero in a zero in equals one and equals two and equals three and equals four and in equals five. So we know that our in equals four. So this is the number that we're interested in. So what do you do with this? Well you do you write out your formula, it's the same formula that you would write out this way, but instead you're given the coefficients. So the first thing is you do A four. So that is the probability that all four of the Children would be males. There's a second choice, right? There's a chance that three would be males, but one would be a female, just four. The 3rd 1 is six and that would be too would be males and two would be females. The other choice use this one. So you see we're just going across 1464 and this will be one at the end. But the next probability is that one is male and three or females. And then finally the last is that all four females and these are all the options of the Children. Now if I were to do this, fill this in with one half for each one of these, this would be um this would equal to one, but we're not interested in what all of this equals, what we're interested in is what is the probability that a family of four Children has two male and two female. So which one of these represents? Two males and two females? Right? It's this one right here because you have two males and two females. So what you do is you take this and that is the probability of having two males and two females and you just solve for it. So we know that it's one half for A each A and B. And so the probability here is 38. So that is one option of solving this problem. The second option is using a different formula and that's this formula. So again you have to solve for in um and it's the total number events which we know right, which we talked about before. So there's a formula here to calculate it which is S. Plus T. S meaning the number of times A occurs which in this case is to because there's two males and T. Is the number of columns B. Occurs which is two because there's two females, so in equals four, same thing as above. And so then you use this problem. So in S. Four S. Is two T. Is two and then you have A. And B. Which are both one half um to the S and T. Which are two and two. So if you were to solve this problem with your calculator you would also get P equals three eights. So it doesn't matter which way you do it. I tend to like this one because I think it requires less math and less formulas because you know all the coefficients are given to you and as long as each one of these adds up to four then you're good to go. But some people don't prefer that way some people prefer, you know just using this formula here to calculate it. But either way it'll get you that probability. And remember this is the type of probability when there's some type of combinations of events happening. And there's all these different alternative ways that it could happen. Um So in this case there's four Children um and there's you know this way they all four could be males, three could be males, two females, one could be males. Are all four could be females. A bunch of different alternative ways and combinations of events that could happen in the production of these Children. But what you're interested in is that 42 are male and two are female. So again it's the by mental math here is a little confusing. You may have to watch it again to fully understand. Um But it is something that you'll likely at least have one question on on a test setting. Um So make sure you understand it. So with that let's not move on.
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Problem

Use the product law to calculate the probability that mating two organisms with the genotype of AaBbCcDd will produce offspring with the genotype of AA bb Cc Dd?

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Problem

In a family of five children what is the probability that… I. Three are males and two are females

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Problem

In a family of five children what is the probability that… All are females

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Problem

In a family of five children what is the probability that… Two are males and three are females

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Problem

In a family of six children, where both parents are heterozygous for albinism, what is the probability that four are normal and two are albinos?

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