# The Multiplication Rule & Mendelian Inheritance

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• 0:01 Probability and Inheritance
• 0:25 Probability Review
• 2:03 Multiplication Rule
• 4:02 Lesson Summary
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Lesson Transcript
Instructor: Artem Cheprasov

Artem has a doctor of veterinary medicine degree.

In this lesson, you're going to learn about basic concepts of probability and how they are applied to Mendelian inheritance with respect to the multiplication rule.

## Probability and Inheritance

Have you ever rolled any dice or tossed some coins and wondered what the chances are that a particular side would come up? You were intrinsically wondering about the probability, or quite simply, the possibility that an event will occur, with respect to a certain frequency with which the event is likely to occur. Concepts of probability can be applied to Mendelian inheritance using something known as the multiplication rule.

## Probability Review

Before we get to this, let's have a very brief review of concepts related to probability:

• Any event that is certain to occur has a probability of 1
• Any event that is certain to not occur has a probability of 0

For instance, let's say you have a coin that has tails on both sides. The probability that it will land on tails after you flip it is 1. Of course, in a normal coin that probability is only ½. The sum of all the probabilities for all the possible outcomes have to add up to 1. In this example we have two outcomes, head or tails. Each outcome has a probability of ½. Therefore, ½ + ½ = 1.

What you probably realize intrinsically is that each flip of the coin is independent of the prior flip. You know that the outcome of the current flip is not influenced by the outcome of the prior flip. Nor would the outcome of the flip of one coin be influenced by the outcome of the flip of another coin if they're flipped simultaneously. This means each coin toss is an independent event because the outcome of any toss is unaffected by the outcome of any prior toss(es), or the simultaneous toss of another coin.

This is important to note because according to Mendel's second law, the law of independent assortment, the alleles of one gene segregate into gametes independently of the alleles of another gene. Confused? Well, if you were to flip a penny and get heads, will that influence if you get heads or tails when you flip a nickel after that? Of course not! Same thing here, except we're dealing with a pair of alleles of a gene instead of a pair of sides of a coin.

## Multiplication Rule

Now, what are the chances that two or more independent events will occur together in a specific fashion? Meaning, if we were to flip the penny and nickel at the same time, what are the chances that, say, both simultaneously land on heads?

In order to figure this out, we need to use the multiplication rule, the multiplication of the probability of one event by the probability of the other event. What's the probability of the penny landing on heads? ½. What's the probability of the nickel landing on heads? ½. So, ½ * ½ = ¼.

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