Question

Imagine that you have developed a genetic test to detect the dominant allele (A) that cause a rare genetic condition. As with most clinical tests, it isn't perfect. When a person does have the dominant allele (Aa or especially rarely AA) your test detects it 100% of the time. But, 0.5% of people who are homozygous recessive (aa) also test positve by your test. Assume 1 out of every 100 people in a population has the dominant allele (Aa or AA).
What percentage of the population will give a positive test?

(A) 0.495%,
(B) 1.495%,
(C) 1.000%,
(D) 99.000%,
(E) 98.505%,
(F) 99.505%

Answer 1

Answer:

Correct option: (B) 1.495%.

Step-by-step explanation:

Denote the events as follows:

X = the test is positive.

A = a person with the dominant allele

The information given are:

$P(X|A)=1\\P (X|A^{c})=0.005\\P(A)=0.01$

According to the law of total probability the probability of an event A, conditional upon the occurrence of another event B is:

$P(A)=P(A|B)P(B)+P(A|B^{c})P(B^{c})$

Use this law to compute the probability of person having a positive result as follows:

 $P(X)=P(X|A)P(A)+P(X|A^{c})P(A^{c})\\=(1\times0.01)+(0.005\times(1-0.01))\\=0.01+0.00495\\=0.01495$

The percentage of positive result is: 0.01495 × 100 = 1.495%.

Thus, the percentage of the population will give a positive test is 1.495%.