Question

Events A and C are independent. If the probabilities relating A, B, and C are P(A) = 1/5, P(B) = 1/6; $P (A \cap C) = 1 / 20$ ; $P (B \cup C) = 3 / 8$ . Then

Moderate

Solution

$P (A \cap C) = P (A) P (C)$
or $\frac{1}{20} = \frac{1}{5} P (C)$
or $P (C) = \frac{1}{4}$
Now,
$P (B \cup C) = \frac{1}{6} + \frac{1}{4} - P (B \cap C)$
$P (B \cap C) = \frac{5}{12} - \frac{3}{8} = \frac{1}{24} P (B) P (C)$
Therefore, B and C are independent.

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