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 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.