`X` speaks truth in 60% and `Y` in 50% of the cases. Find the probability that they contradict each other narrating the same incident.

Options

A. `(1)/(4)`
B. `(1)/(4)`
C. `(1)/(2)`
D. `(2)/(3)`

Answer

C

Explanation

Consider the following events :
A=X speaks truth, B=Y speaks truth.
Then, `P(A)=(60)/(100)=(3)/(5) " and " P(B)=(50)/(100)=(1)/(2)`
Required probability `=P((A cup overline(B))cup (overline(A) cap B))`
`P(A cap overline(B))+P(overline(A) cap B)`
`=(3)/(5)xx(1)/(2)+(2)/(5)xx(1)/(2)=(1)/(2)`