Two independent events A and B have `P(A) = (1)/(3)` and `P(B) = (3)/(4)` What is the probability that exactly one of the two events A or B occurs?

Options

A. `(1)/(4)`
B. `(5)/(6)`
C. `(5)/(12)`
D. `(7)/(12)`

Answer

D

Explanation

A and B are independent.
`P(A) = (1)/(3) " "P(B) = (3)/(4)`
We want to find probability that exactly one of the two events A or B occurs i.e. when A occurs B does not and Vice-versa.
Lets take desired prob. is P.
`therefore P = P(A) (1-P(B)) + P(B) (1-P(A))` ltbr gt `= (1)/(3) (1-(3)/(4)) +(3)/(4)(1-(1)/(3))`
`= (1)/(3) xx (1)/(4) +(3xx2)/(12)`
` P = (7)/(12)`