Question

The probability that A speaks truth is $\frac { 4 } { 5 }$ , while this

probability for B is $\frac { 3 } { 4 }$ . The probability that they contradict

each other when asked to speak on a fact is

• A. $\frac { 4 } { 5 }$
• B. $\frac { 1 } { 5 }$
• C. $\frac { 7 } { 20 }$
• D. $\frac { 3 } { 20 }$

Answer 1

Answer: (C)

$\frac { 7 } { 20 }$

Answer 2

Let E be the event that B speaks truth and F be the event that A speaks truth.

Now $P ( E ) = \frac { 75 } { 100 } = \frac { 3 } { 4 }$ and $P ( F ) = \frac { 80 } { 100 } = \frac { 4 } { 5 }$.

∴ P (A and B contradict each other)

= P [(B tells truth and A tells lie) or (B tells lie and A tells truth)]

.