# A speaks truth in 80% of the cases and B speaks truth in 60% of the cases. Find the probability that they contradict each other in narrating an incident - Mathematics and Statistics

Sum

A speaks truth in 80% of the cases and B speaks truth in 60% of the cases. Find the probability that they contradict each other in narrating an incident

#### Solution

Let event A : A speaks the truth,

event B : B speaks the truth.

∴ P(A) = 80/100 = 4/5

and P(B) = 60/100 = 3/5

∴ P(A') = 1 – P(A) = 1 - 4/5 = 1/5

and  P(B') = 1 – P(B) = 1 - 3/5 = 2/5

∴ P(A and B contradict each other)

= P(A speaks the truth and B lies) + P (A lies and B speaks the truth)

= P(A ∩ B') + P(A' ∩ B)

= P(A) P(B') + P(A') P(B)

= (4/5 xx 2/5) + (1/5 xx 3/5)

= 8/25 + 3/25

= 11/25.

Concept: Multiplication Theorem on Probability
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