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One hundred students appeared for two examinations 60 passed in first, 50 passed the second and 30 passed both. The probability that a student selected at random has failed in both examinations is

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$\frac{1}{5}$

$\frac{4}{5}$

$\frac{3}{5}$

$\frac{1}{7}$

answer is A.

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Detailed Solution

$P (A \cup B) = \frac{60}{100} + \frac{50}{100} - \frac{30}{100} = \frac{80}{100}$

$P (A' \cap B') = P (A \cup B)' = 1 - P (A U B)$

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