Maharashtra State BoardHSC Science (Electronics) 11th
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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

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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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