# A geneticist is studying two genes. Each gene can be

## Problem 17E Chapter 2.3

Statistics for Engineers and Scientists | 4th Edition

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Problem 17E

A geneticist is studying two genes. Each gene can be either dominant or recessive. A sample of 100 individuals is categorized as follows.

 Gene2 Gene1 Dominate Recessive Dominate 56 24 Recessive 14 6

a. What is the probability that a randomly sampled individual, gene 1 is dominant?

b. What is the probability that a randomly sampled individual, gene 2 is dominant?

c. Given that gene 1 is dominant, what is the probability that gene 2 is dominant?

d. These genes are said to be in linkage equilibrium if the event that gene 1 is dominant is independent of the event that gene 2 is dominant. Arc these genes in linkage equilibrium?

Step-by-Step Solution:

Step 1:

A study about two genes done by a geneticist. Each gene can either be recessive or dominant.

A sample of 100 individuals categorized as

 Gene 2 Gene 1 Dominate Recessive Total Dominate 56 24 80 Recessive 14 6 20 Total 70 30 100

We have to find

The probability that a randomly sampled individual, gene 1 is dominant.The probability that a randomly sampled individual, gene 2 is dominant.Given that gene 1 is dominant, then the probability that gene 2 is dominant.Genes are said 2 to equilibrium if the event that gene 1 is dominant and gene 2 is dominant are independent. Is this events are independent.

Step 2:

From the table we can find that

P(that a randomly sampled individual , gene 1 is dominant) =

=

=   0.8

Therefore probability that a randomly sampled individual, gene 1 is dominant = 0.8.

(b)

The probability that randomly selected individual , gene 2 is dominant

P( that randomly selected individual , gene 2 is dominant) =

=

=  0.7

Therefore the probability that a randomly selected individual, gene 2 is dominant = 0.7.

Step 3 of 4

Step 4 of 4

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