The probability of an event B is P_B. The probability that events A and B occur together is P_{AB} while the probability that A and B' (complement of B) occur together is P_{AB'}. The probability of the event A in terms of P_B, P_{AB}, and P_{AB'} is ___________.
GATE 1994 · Engineering Mathematics · Conditional Probability · medium
Answer: P(A) = P_{AB} + P_{AB'}
Apply the law of total probability: Since B and B' are complementary and mutually exclusive, P(A) = P_{AB} + P_{AB'}.
State the result: The answer is P(A) = P_{AB} + P_{AB'}. Note that P_B itself does not appear explicitly in the final expression because the given joint probabilities already encode the conditioning on B and B'.