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FRM Part I · FRM Exam Part I · Fundamentals of Probability

Events A and B are mutually exclusive with P(A) = 0.40 and P(B) = 0.35. Event C is the complement of the union of A and B. What is P(C), and are A and B independent?

P(C) is 0.25 and A and B are not independent. Since A and B are mutually exclusive, P(A or B) is 0.75, so the complement is 0.25. Independence would need a joint probability of 0.14, but it is zero, so the events are dependent.

  1. AP(C) = 0.25; A and B are not independentCorrect
  2. BP(C) = 0.25; A and B are independent
  3. CP(C) = 0.14; A and B are independent
  4. DP(C) = 0.75; A and B are not independent

Explanation

Mutually exclusive means P(A∪B) = 0.75, so P(C) = 1 − 0.75 = 0.25. Independence would require P(A∩B) = 0.40×0.35 = 0.14, but mutually exclusive events have P(A∩B) = 0, which differs, so they are not independent.

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