 Hello again, and welcome to the next installment of genetics. In this lecture, we're going to be focusing on the laws of probability. Now, if any of you have ever gone gambling, I'm sure you've realized that the laws of probability when it comes to gambling and money are almost always against you. However, believe it or not, they can actually be pretty useful when it comes to figuring out what the genotypes and phenotypes will be in the next generation. But let's step back a minute and take a look at an example that everybody can pretty much relate to. Dive into your pocket and pull out whatever coin you may have inside. So if it's a penny, a quarter, a nickel, a dime, if it's in my pocket, most likely it's just going to be a penny. So pull out your penny. And if you were to flip this coin in the air and let it land, you would realize that you have a half a chance of getting heads and you have a half a chance of getting tails. And this is for one coin. This is pretty simple. But what about two coins? Let's say you wanted to know the probability if you were to flip two coins of getting two heads. Alright, let's work through this, but let's take each coin separately. For coin one you'd have a half a chance of getting heads and a half a chance of getting tails. For coin two, you would have half a chance of getting heads and half a chance of getting tails. So for the purpose of this particular lecture and when it comes to probability what I would like you to remember is whenever you see the word and you're going to multiply. If ever you see the word or you're going to add. And I'll show you what I mean in a second. We want to know the probability of getting heads for the first coin and heads for the second coin. Which would be one half and so you would multiply times one half. This gives you a fourth. So what's the probability of getting one head and one tail in any order? Okay, well you have a half a chance of getting a head from the first coin and a half a chance of getting a tail from the second coin. So it's a half times a half. Or you could also get a half a chance of a tail from the first coin and a half a chance of a head from the second coin. Remember we said if it was or you're going to add one half times one half. Alright. So one half times one half is a fourth plus one half times one half which is another fourth is equal to two fourths or one half. Now let's work through the last example. The probability of getting two tails of course is going to be one half for the first coin and one half for the second coin. So it's a half times a half again which gives you a fourth. Now let's actually relate this to Mendel's work and the Punnett Square. If you recall when we were talking about Mendel's crosses you remember that his first filial generation was heterozygous for purple flower color. So it had one big pea, one little pea in the first plant and a big pea, little pea in the second plant. Now according to the law of segregation when gametes are formed they have half the number of chromosomes as the individual that they came from. This is how we make the system make sure that there's exactly the right number of chromosomes for the next generation. So there's a half a chance of getting a big pea and a half a chance of getting a little pea. So if we were to actually draw this out in our Punnett Square for the first individual we have a half a chance of a big pea, half a chance of a little pea in the second individual we have a half a chance of a big pea, half a chance of a little pea. So the probability of getting a big pea, big pea is going to be a fourth. Probability of a big pea, little pea is going to be a fourth. Probability of a little pea, big pea is going to be a fourth. And the probability of a little pea, little pea is going to be a fourth. So we have a fourth of a chance of a big pea, big pea. Now the probability of being heterozygous, remember, this could be in any order. So it's a fourth of a chance of a little p, big p, and, which case you have a fourth of a chance of a big p, little p, okay? But you could have this combination or this combination. Remember when we said you see the word or, you want to add them. So it's two fourths of a big p, little p in any combination. And then one fourth of a little p, little p, okay? So this is a 1 to 2 to 1 ratio or this is a 3 to 1. And remember that correlates with what we talked about in the last lecture. Except this time we figured it out using the laws of probability.