The probability that `A` speaks truth is `(4)/(5)`, while this probability for `B` is `(3)/(4)`. The probability that they contradict each other when asked to speak on a fact is ____

Options

A. `(4)/(5)`
B. `(1)/(5)`
C. `(7)/(20)`
D. `(3)/(20)`

Answer

C

Explanation

Consider the following events :
E=A speaks truth, F=B speaks truth.
We have, `P(E )=(4)/(5) " and " P(F)=(3)/(4)`
Required probability `=P((E cap overline(F)) cup (overline(E ) cap F))`
`=P(E cap overline(F))+P(overline(E ) cap F)`
`=P(E ) P(F)+P(overline(E )) P(F)`
`=(4)/(5)xx(1-(3)/(4))+(1-(4)/(5))xx(3)/(4)=(7)/(20)`