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A geneticist is studying two genes. Each gene can be

Statistics for Engineers and Scientists | 4th Edition | ISBN: 9780073401331 | Authors: William Navidi ISBN: 9780073401331 38

Solution for problem 17E Chapter 2.3

Statistics for Engineers and Scientists | 4th Edition

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Statistics for Engineers and Scientists | 4th Edition | ISBN: 9780073401331 | Authors: William Navidi

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

Chapter 2.3, Problem 17E is Solved
Step 4 of 4

Textbook: Statistics for Engineers and Scientists
Edition: 4
Author: William Navidi
ISBN: 9780073401331

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