A speaks truth in 75% cases and B speaks truth in 80% cases. The probability that they contradicts each other in a statement is :

$\frac{7}{20}$

The correct answer is Option (1) → $\frac{7}{20}$

Probability of A to speaks the truth = $P(A_T)=0.75$

Probability of A to speaks the lie = $P(A_F)=0.25$

Probability of B to speaks the truth = $P(B_T)=0.80$

Probability of B to speaks the lie = $P(B_F)=0.20$

A speaks truth while B lies = $P(A_T)×P(B_F)$

$=0.75×0.20=0.15$

A lies while B speaks truth = $P(A_F)×P(B_T)$

$=0.25×0.80=0.20$

P (contradiction) = 0.20 + 0.15 = 0.35