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An employer sends letter to his employee but he doesn’t receive the reply (It is certain that the employee would have replied, if he did receive the letter). It is known that one out of 10 letters doesn’t reach its destination. Then the probability the employee does not receive the letter is

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$\frac{9}{19}$

$\frac{10}{20}$

$\frac{10}{27}$

$\frac{7}{23}$

answer is A.

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Detailed Solution

(1) E = employee receive the letter
A = employer receive the reply
$P (E) = \frac{9}{10} P (\bar{E}) = \frac{1}{10}$
$P (A) = P (E) . P (A | E) + P (E) . P (A | \bar{E})$
Required probability $= P (E | \bar{A}) = \frac{9}{19}$

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