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VladimirAG [237]
3 years ago
14

Imagine that you have developed a genetic test to detect the dominant allele (A) that cause a rare genetic condition. As with mo

st 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%
Mathematics
1 answer:
s344n2d4d5 [400]3 years ago
4 0

Answer:

Correct option: (B) 1.495%.

Step-by-step explanation:

Denote the events as follows:

<em>X</em> = the test is positive.

<em>A</em> = 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 <em>A, </em>conditional upon the occurrence of another event <em>B</em> 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%.

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