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The probability that A speaks truth is (...

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

A

`(4)/(5)`

B

`(1)/(5)`

C

`(7)/(20)`

D

`(3)/(20)`

Text Solution

Verified by Experts

The correct Answer is:
C
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)`
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