Given:

⇒ Husband tells lies in 30% of cases

⇒ Wife tells lies in 35% of cases

Now,

⇒ P(N_H) = P(Husband telling lies) = 0.30

⇒ P(T_H) = P(Husband telling truth) = 1-0.30

⇒ P(T_H) = 0.70

⇒ P(N_W) = P(Wife telling lies) = 0.35

⇒ P(T_W) = P(Wife telling truth) = 1-0.35

⇒ P(T_W) = 0.65

We need to find the probability for case in which husband and wife contradict each other for narrating a fact.

This happens only when husband not telling truth while Wife is telling truth and vice-versa.

⇒ P(C_HW) = P(Husband and Wife contradict each other)

⇒ P(C_HW) = P(Husband tells truth and Wife doesn’t) + P(Wife tells truth and Husband doesn’t)

Since the speaking of husband and Wife are independent events their probabilities will multiply each other.

⇒ P(C_HW ) = (P(T_H)P(N_W)) + (P(N_H)P(T_W))

⇒ P(C_HW) = (0.70×0.35) + (0.30×0.65)

⇒ P(C_HW) = 0.245 + 0.195

⇒ P(C_HW) = 0.44

∴ The required probability is 0.44.