Question

Type O blood donors ("universal donors") are the most useful, because their blood can be transfused into patients with blood type O, A, B, or AB. The allele frequency of the O allele in the U.S. population is 2/3. The U.S. population is in Hardy-Weinberg equilibrium for blood type. What is the frequency of people with the type O blood type in the U.S. population?

A. 1/3
B. 1/4
C. 1/9
D. 2/9
E. 4/9

Answer 1

option E.
`(4)/(9)`

Step-by-step explanation:

According to the question,

Allele frequency of the 'O' allele in the US population ,p =
`(2)/(3)`

Therefore, frequency for the rest of the patients, q = 1 - p =
`1 - (2)/(3) = (1)/(3)`

Hardy- Weinberg equilibrium condition states that in absence of the factors that can cause disturbance, the amount or extent of variation in genes in a population will not vary (constant) throughout the generations.

Therefore,

p + q = 1

In accordance to Hardy- Weinberg equilibrium eqn:

`p^(2) + 2pq + q^(2) = 1` (1)

where,

`p^(2)` = homozygous dominant

`q^(2)` = homozygous recessive

2pq = heterozygous

Using eqn (1)

`((2)/(3))^(2) + 2((2)/(3))((1)/(3)) + ((1)/(3))^(2) = 1`

`(4)/(9) + (4)/(9) + (1)/(9) = 1`

Therefore, the frequency of people with blood type 'O' in the U.S. population is
`p^(2) = (4)/(9)`