Question

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

Options

• `4/5`

• `1/5`

• `7/20`

• `3/20`

Answer 1

The probability that A speaks truth is `4/5`, while the probability for B is `3/4`. The probability that they contradict each other when asked to speak on a fact is `underlinebb(7/20)`.

Explanation:

A and B will contradict each other if one speaks the truth and the other false.

So, the required probability

`P(A ∩ overlineB) + P(overlineA ∩ B) = 4/5(1 - 3/4) + (1 - 4/5)3/4`

= `4/5 xx 1/4 + 1/5 xx 3/4`

= `7/20`