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

Options

A. `(75)/(107)`
B. `3/5`
C. `15/19`
D. `3/10`

Answer

A

Explanation

`((1)+(3))/((1)+(3)+(5)+(7))`
`((3)/(5)xx(1)/(2)xx(4)/(5)+(3)/(5)xx(1)/(2)xx(1)/(5))/((3)/(5)xx(1)/(2)xx(4)/(5)+(3)/(5)xx(1)/(2)xx(1)/(5)+(2)/(5)xx(1)/(5)xx(4)/(5)+(2)/(5)xx(4)/(5)xx(1)/(5))`
`((3)/(10))/((3)/(10)+(16)/(125))`
`(75)/(107)`