# Rules of Addition and Multiplication – Beyond Gregor Mendel

by Georgina Cornwall, PhD

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00:01 In this lecture, we will continue our investigation of classical genetics by looking a little bit beyond Mendel. We will be looking at Mendelian inheritance patterns that don't quite exhibit the expected ratios. This isn’t that Mendel is wrong; they are just extensions of his concepts. By the end of this lecture, you will be able to predict the outcomes of mono and dihybrid crosses using probability methods as well as interpret test cross data to determine unknown phenotypes and finally you will be able to explain why not all crosses exhibit Mendel's predicted phenotypic outcomes. First let us begin by looking at probabilities.

00:45 We can predict the outcome of test crosses using a much simpler method really than Punnett squares. Some of us get hooked on Punnett square, but realistically probability methods are a much more simple way to go about it. I don't know how much experience you've had with probability, but we will take a quick look at two rules. One is the rule of addition and one is the rule of multiplication. And these are rules that really allow us to turn sentences into mathematical equations. The rule of addition states that two mutually exclusive events, the probability of either event occuring is the sum of their two probabilities.

01:27 Now that seems like a lot of words. Let us look at an example so that you can see what we mean exactly. Let us say you have one six sided dice and you want to roll that dice and get either a 1 or 2 or 3 or 5 or 6. Well you probably already have a pretty good idea that no matter what six sided dice you roll with six numbers on them, you are very likely to get one of those numbers as in 100 percent of the time unless it balances on a corner something strange. You will get either one of these six numbers. Let us take a look at that mathematically. There is a probability of one sixth that we could get a number of 1 or there is a probability that we could get a number 2, 1/6 or we could get a 3 or a 4 or a 5 or a 6. When we sum these probabilities indeed, we do find that the math verifies that we have a 100 percent probability of rolling 1 of the 6 sides of the dice. The addition rule means OR. Any time you see OR or can stuff an OR into a sentence it means you are getting to add the probabilities of the independent events. Now let us look at the rule of multiplication.

02:52 This is an AND rule. Anytime you can stuff an AND in, we will multiply. It states that the probability of two independent events both occurring is the product of their individual probabilities. Let us take a look at that on a dice so that we can put some meaning behind all those crazy words. Let us say we have two dice this time and you want to roll a 1 and a 6. There is a one-sixth probability of rolling 1 and on the second dice and you want to roll the 6. We have 1/6 x 1/6 and that gives us 1/36 chance of doing it exactly this way. We can have a 1 and then a 6. AND really means to multiply. Anytime you can jam AND into a sentence for more thinking about probability, you are going to multiply the two probabilities. Any time you can put a OR in and you will add them. You don’t really need to know the specific language of the probability law just the AND and OR part.

### About the Lecture

The lecture Rules of Addition and Multiplication – Beyond Gregor Mendel by Georgina Cornwall, PhD is from the course Understanding Genetics.

### Included Quiz Questions

1. …addition and multiplication rules.
2. …addition and subtraction rules.
3. …subtraction and product rules.
4. …addition and division rules.
5. …product and division rules.
1. …multiplying the individual probabilities of the events.
2. …dividing the individual probabilities of the events with each other.
3. …subtracting the individual probabilities of the events from the number 100.
4. …adding the individual probabilities of the events.
5. …adding the individual probabilities of the events with the product value.

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