Question

In a family, the husband tells a lie in 30% cases and the wife in 35% cases. Find the probability that both contradict each other on the same fact.

 

Answer 1

It is given that the husband lies in 30% of the cases, while the wife lies in 35% cases

\[P\left( \text{ both will contradict each other on the same fact } \right) = P\left( \text{ husband lies but wife tells the truth }  \right) + P\left( \text{ wife lies buthusband tells the truth }  \right)\]
\[ = 0 . 3 \times \left( 1 - 0 . 35 \right) + \left( 1 - 0 . 3 \right) \times 0 . 35\]
\[ = 0 . 3 \times 0 . 65 + 0 . 7 \times 0 . 35\]
\[ = 0 . 195 + 0 . 245\]
\[ = 0 . 44\]

`= 44 %`