Two men hit at a target with probabilityes `(1)/(2) and (1)/(3)` respectively. What is the probability that exactly one of the them hits the target.

Options

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

Answer

A

Explanation

`P=P(E_(1))P(overset(_)E_(1))P(overset(_)E_(2))P(E_(2))`
`=(1)/(2)(1-(1)/(3))+(1-(1)/(2))(1)/(3)`
`=(1)/(2)xx(2)/(3)+(1)/(2)xx(1)/(3)`
`=(1)/(3)+(1)/(6)=(1)/(2)`
`therefore` Option (a) is coorect.