Q. 135.0( 2 Votes )

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.


Rate this question :

How useful is this solution?
We strive to provide quality solutions. Please rate us to serve you better.
Try our Mini CourseMaster Important Topics in 7 DaysLearn from IITians, NITians, Doctors & Academic Experts
Dedicated counsellor for each student
24X7 Doubt Resolution
Daily Report Card
Detailed Performance Evaluation
view all courses
RELATED QUESTIONS :