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What is the correct answer?

4

A speaks truth in 75% of cases and B in 80% of cases. In what percentage of cases are they likely to contradict each other, narrating the same incident

A. 30%

B. 35%

C. 40%

D. 45%

Correct Answer :

B. 35%



Let A = Event that A speaks the truth
B = Event that B speaks the truth
Then P(A) = 75100 = 34
P(B) = 80100= 45
P(A-lie) = 1-34 = 14
P(B-lie) = 1-45= 15
Now, A and B contradict each other = [A lies and B true] or [B true and B lies]
= P(A).P(B-lie) + P(A-lie).P(B)
[Please note that we are adding at the place of OR]
35×15+14×45= 720
720 × 100% = 35%

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