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Q.

A speaks truth in 75% of the cases and B in 80% of the cases. Then the probability that their statements about an incident do not match, is

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a

3/20

b

5/7

c

7/20

d

2/7

answer is A.

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Detailed Solution

$P (A) = \frac{75}{100} = \frac{3}{4}, P (B) = \frac{80}{100} = \frac{4}{5}$ and $A, B$ are independent
$P [(A - B) \cup (B - A)] = P (A - B) + P (B - A) = P (A \cap B) + P (\bar{A} \cap B) = P (A) P (\bar{B}) + P (\bar{A}) P (B) = \frac{3}{4} \times \frac{1}{5} + \frac{1}{4} \times \frac{4}{5} = \frac{7}{20}$

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