Mark the correct alternative in the following question:

$If A and B are two events such that P (A) \neq 0 and P (B) \neq 1, then P (A | B) = (a) 1 - P (A | B) (b) 1 - P (A | B) (c) \frac{1 - P (A \cup B)}{P (B)} (d) \frac{P (A)}{P (B)}$

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Solution

$We have, P (A) \neq 0 and P (B) \neq 1 Now, P (A | B) = \frac{P (A \cap B)}{P (B)} = \frac{P (A \cup B)}{P (B)} = \frac{1 - P (A \cup B)}{P (B)}$

Hence, the correct alternative is option (c).

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