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A man A speaks truth in 80% of the cases and another man B in 90% of the cases. While stating the same fact, what is the probability that they contradict?

(a) \(\frac{37}{50}\)

(b) \(\frac{13}{50}\)

(c) \(\frac{16}{50}\)

(d) None of these

1 Answer

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Best answer

(b) \(\frac{13}{50}\)

Probability (contradiction) = P(A speaks truth) × P(B does not speak truth) + P(A does not speak truth) × P(B speaks truth)

\(\frac{80}{100}\times\frac{10}{100}\) + \(\frac{20}{100}\times \frac{90}{100}\)

\(\frac{8}{100}\)\(\frac{18}{100}\) = \(\frac{26}{100}\) = \(\frac{13}{50}\)

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