Question

Genetics: 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			Recessive
Gene 1	Dominant	57	20
	Recessive	14	9

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(a) What is the probability that in a randomly sampled individual, gene

1

is dominant?

(b) What is the probability that in 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) Two 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. Are these genes in linkage equilibrium?

The probability that gene 1 is dominant in a randomly sampled individual is

.

Answer 1

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

Solution:

Gene 1/Gene 2	Dominant	Recessive	Total
Dominant	57	20	77
Recessive	14	9	23
Total	71	29	100

(a) the probability that in a randomly sampled individual is gene 1 is dominant:

P(gene1 dominant)

= no. of gene1 dominant / total no. Of individual

= 77/100

= 0.7700

(b) the probability that in a randomly sampled individual, gene 2 is dominant:

P(gene 2 dominant)

= no. of gene 2 dominant / total no. of individual

= 71/100

=0.7100

(c) Given that gene 1 is dominant, the probability that gene 2 is dominant:

P(gene2 dominant | gene 1 dominant)

= P(gene 2 dominant and gene 1 dominant) / P(gene 2 dominant)

= (57/100) /( 77/100)

= 57/77

= 0.74026

≅ 0.7403

(d) Two 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. Are these genes in linkage equilibrium?

By using definition of independent events

P(B|A) = P(B)

P(gene 2 dominant and gene 1 dominant) = P(gene 2 dominant)

0.7403 ≠ 0.7100

The events gene 1 is dominant and gene 2 dominant are not independent.

Therefore, the genes are not in linkage equilibrium.

.