A committee of two persons is selected from two men and two women. The probability that the committee will have exactly one woman is.

Options

A. `(1)/(6)`
B. `(2)/(3)`
C. `(1)/(3)`
D. `(1)/(2)`

Answer

B

Explanation

We know, `P(E) = ("No.of favourable outcomes")/("Total no.of outcomes")`
Number of possible outcome `= ""^(4)C_(2) = (4 xx 3)/(2xx 1) = 6`
(selecting 2 people form 4 people) .
Number of favourable outcomes.
`= ""^(2)C_(1) xx""^(2)C_(1) = 2xx 2 = 4`
(Selecting 1 form 2 men , 1 form 2 women).
`P(E) = (4)/(6) = (2)/(3)`.