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. 3/23
• B. 1/20
• C. 1/5
• D. 14/40

Answer 1

The correct option is D 14/40

In short the event described here is P(A)'P(B) +P(A)P(B)'

where P(A) and P(B) are the probabilities of A and B speaking the truth.

P(A)' and P(B)' are the probabilities of A and B not speaking the truth.

$P(A{)}^{\prime }=1-P(A)=1-\frac{4}{5}=\frac{1}{5}$

$P(B{)}^{\prime }=1-P(B)=1-\frac{3}{4}=\frac{1}{4}$

$P\left(E\right)=\frac{1}{5}\times \frac{3}{4}+\frac{4}{5}\times \frac{1}{4}$

$P\left(E\right)=\frac{3}{20}+\frac{4}{20}=\frac{7}{20}=\frac{14}{40}$