Question

A geneticist is studying two genes. Each gene can be either dominant or recessive. A sample of 100 individuals is categorized as follows. Write your answer as a fraction or a decimal, rounded to four decimal places.

Gene 2.  

	Dominant(gene 2)	Recessive(gene 2)
Dominant gene1	53	27
recessive gene 1	17	3

Gene 1

(a) What is the probability that in a randomly sampled individual, gene 1 is recessive? (b) What is the probability that in a randomly sampled individual, gene 2 is recessive? (c) Given that gene 1 is recessive, what is the probability that gene 2 is recessive? (d) Two genes are said to be in linkage equilibrium if the event that gene 1 is recessive is independent of the event that gene 2 is recessive. Are these genes in linkage equilibrium?

Answer 1

	Dominant (G2)	Recessive (G2)	total
Dominant (G1)	53	27	80
Recessive (G1)	17	3	20
total	70	30	100

a) Probability that Gene 1 is recessive = 20 /100 =0.2

Note : This is marginal probability , thus we find it by dividing marginal total ( row total for gene 1 ) by grand total

b) Probability that Gene 2 is recessive=30 /100= 0.3

Note : This is marginal probability , thus we find it by dividing marginal total ( column total for gene 2 ) by grand total

c) P ( Gene 2 recessive I Gene 1 recessive )

= P( Both Gene 1 and Gene 2 recessive ) / P( Gene 1 recessive)

= (3/100) / (20 /100)

= 0.15

Note : This is conditional probability , we find it by dividing joint probability / marginal probability

d) Event of Gene 1 recessive and Gene 2 recessive are said to independent if

P ( Gene 2 recessive I Gene 1 recessive ) = P( gene 2 recessive)

(that is conditional probability of Gene 2 recessive =un conditional probability Gene 2 recessive)

But , P ( Gene 2 recessive I Gene 1 recessive ) = 0.15

and P( gene 2 recessive) = 0.3

Thus the events Gene 1 recessive and Gene 2 recessive are not independent

The two genes are not in linkage equlibrium .