Question

A speaks truth in 60% cases and B speaks truth in 70% cases. The probability that they will say the same thing while describing a single event is

• A. 0.56
• B. 0.54
• C. 0.38
• D. 0.94

Answer 1

The correct option is B 0.54

$P\left(A\right)=\frac{60}{100}=\frac{3}{5},P\left(\overline{A}\right)=1-\frac{3}{5}=\frac{2}{5}P\left(B\right)=\frac{70}{100}=\frac{7}{10},P\left(\overline{B}\right)=1-\frac{7}{10}=\frac{3}{10}$
Probability of getting same result in single event
$=P\left(A\right).P\left(B\right)+P\left(\overline{A}\right)P\left(\overline{B}\right)=\frac{3}{5}\times \frac{7}{10}+\frac{2}{5}\times \frac{3}{10}=\frac{27}{50}=0.54$