A and B are two independent witnesses in a case. The probability that A will speak the truth is 1/3 and the probability that B will speak the truth is - Mathematics MCQ Mathematics Mock Test - 10 2026 | ExamTest.live

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A and B are two independent witnesses in a case. The probability that A will speak the truth is 1/3 and the probability that B will speak the truth is 3/4 . If A and B agree on a certain statement, then the probability that the statement is true is:

Solution & Step-by-step Explanation

Let T be the event that the statement is true, and E be the event that A and B agree. P (Truth_{A}) = 1/3, P (False_{A}) = 2/3 P (Truth_{B}) = 3/4, P (False_{B}) = 1/4 A and B agree in two cases:Both speak the truth: P (E ∣ T) = (1/3) \times (3/4) = 1/4 Both lie: P (E ∣ \overset{ˉ}{T}) = (2/3) \times (1/4) = 2/12 = 1/6 Using Bayes' Theorem: P (T ∣ E) = \frac{P ( E ∣ T )}{P ( E ∣ T ) + P ( E ∣ T ˉ )} (Assuming P (T) = P (\overset{ˉ}{T}) as we have no prior info) P (T ∣ E) = \frac{1/4}{1/4 + 1/6} = \frac{1/4}{5/12} = \frac{1}{4} \times \frac{12}{5} = \frac{3}{5}

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A and B are two independent witnesses in a case. The probability that A will speak the truth is 1/3 and the probability that B will speak the truth is 3/4 . If A and B agree on a certain statement, then the probability that the statement is true is:

2/5

3/5

4/5

1/5

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