KVPY SX SB Exam 2018 Question Paper

Question : 15 of 120

Marks: +1, -0

The probability of men getting a certain disease is

1/2

and that of women getting the same disease is

1/5

. The blood test that identifies the disease gives the correct result with probability

4/5

. Suppose a person is chosen at random from a group of 30 males and 20 females, and the blood test of that person is found to be positive. What is the probability that the chosen person is a man ?

$75/104$
$3/5$
$15/19$
$3/10$

Validate

Solution:

Let E be the event that person is found to be positive, M be the event that chosen person is a man and W be the event that chosen person is a woman.

P(E/M)-1/2×4/5+1/2×1/5=1/2

P(E/W)=1/5×4/5+4/5×1/5=8/25

By Baye’s theorem,

P(M/E)={1/2×3/5}/{1/2×3/5+8/25×2/5}=75/107

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