Q142 / 225 · JEE Main 2004 · Mathematics

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
    $\frac{3}{20}$
  • B
    $\frac{1}{5}$
  • Correct answer
    C
    $\frac{7}{20}$
  • D
    $\frac{4}{5}$

Solution

$\mathrm{E}_1$ : event denoting that $A$ speaks truth $\mathrm{E}_2$ : event denoting that $B$ speaks truth Probability that both contradicts each other $=P\left(E_1 \cap \bar{E}_2\right)+P\left(\bar{E}_1 \cap E_2\right)=\frac{4}{5} \cdot \frac{1}{4}+\frac{1}{5} \cdot \frac{3}{4}=\frac{7}{20}$

Hence, the correct answer is option: 'C'.

Relevant Questions