# Using Probability to Solve Complex Genetics Problems

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• 0:00 Coins and Segregation
• 0:54 Probability Images
• 2:35 Probability Math
• 5:08 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 how to use Punnett squares and the multiplication rule to quickly solve complex genetic problems with respect to the law of independent assortment.

## Coins and Segregation

Let's say you have two coins. One is a penny and the other is a quarter. The flip of each coin can get you a pair of possible outcomes, heads or tails. If you flip the penny and get heads, does that result have any bearing on whether or not you'll get a heads or tails when you flip the quarter next? No! That's because these are two independent events.

Instead of flipping coins, when it comes to genetics, when each allele pair segregates during gamete (sex cell) formation, they do so independently as well, according to the Mendel's second law, the law of independent assortment. This means that a multi-character cross is like two or more independent monohybrid crosses that occur at the same time.

Consequently, we can figure out the probability that specific genotypes will occur in the F2 generation using the concepts we're going to go over in this lesson.

## Probability Images

Using the image on your screen (see video), you can see that we have constructed a dihybrid cross between two RrYy F1 heterozygotes. These were derived from a parental generation using a cross between an RRYY and an rryy. The male gametes of the F1 generation, thus turn out to be RrYy and the female gametes of the F1 generation are also RrYy.

R refers to the dominant allele for seed shape, round. Little r refers to the recessive allele for seed shape, wrinkled. Y refers to the dominant allele for seed color, yellow, and little y refers to the recessive allele for seed color, green.

The image has constructed a square to help us figure out the probability of any genotype that may result in the F2 generation. For instance, we can see that, in total, we can have 16 different possible outcomes, ranging from RRYY to rryy.

If I were to ask you, what is the probability that the F2 offspring will be RRYY? You'd look at the square and tell me that it would be 1/16, because only one such possibility exists. If I were to ask you, what is the probability that the offspring are RRYy? You'd tell me it is 1/8, because there are two such possible outcomes, and 2/16 = 1/8.

## Probability Math

Now, how can we use math to more quickly figure all of this out without having to construct a complex image of 16 possible outcomes or look through the square carefully to ensure we didn't miss the genotype in question?

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