Question

$A$ speaks truth in $75\%$ cases and $B$ in $80\%$ cases. What is the probability that they contradict each other in stating the same fact?

• A. $\frac{7}{20}$
• B. $\frac{13}{20}$
• C. $\frac{3}{20}$
• D. $\frac{1}{5}$

Answer 1

The correct option is A $\frac{7}{20}$

Let A = Event that A speaks the truth

B = Event that B speaks the truth

Then $P\left(A\right)=\frac{75}{100}=\frac{3}{4}$

$P\left(B\right)=\frac{80}{100}=\frac{4}{5}$

$P(A-lie)=1-\frac{3}{4}=\frac{1}{4}$

$P(B-lie)=1-\frac{4}{5}=\frac{1}{5}$

Now

A and B contradict each other = [A lies and B true] or [B true and B lies]

$=P\left(A\right).P(B-lie)+P(A-lie).P\left(B\right)⟹\frac{3}{4}\times \frac{1}{5}+\frac{1}{4}\times \frac{4}{5}=\frac{7}{20}$