1.

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»

Given:

⇒ Husband tells lies in 30% of cases

⇒ Wife tells lies in 35% of cases

Now,

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

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

⇒ P(TH) = 0.70

⇒ P(NW) = P(Wife telling lies) = 0.35

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

⇒ P(TW) = 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(CHW) = P(Husband and Wife contradict each other)

⇒ P(CHW) = 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(CHW ) = (P(TH)P(NW)) + (P(NH)P(TW))

⇒ P(CHW) = (0.70 × 0.35) + (0.30 × 0.65)

⇒ P(CHW) = 0.245 + 0.195

⇒ P(CHW) = 0.44

∴ The required probability is 0.44.


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