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Passage: Let A , B , C and D be mutually exclusive and exhaustive events and P(A) 2 = P(B) 3 = P(C) 5 = P(D) 8 . Question: What is [2P(A)+3P(B)] [4P(C)+5P(D)] equal to ?

Options

  1. A13 18
  2. B13 60
  3. C4 21
  4. D5 28

Correct answer

B. 13 60

Step-by-step solution

Let P(A) 2 = P(B) 3 = P(C) 5 = P(D) 8 = k Then P(A) = 2k , P(B) = 3k , P(C) = 5k , and P(D) = 8k Since A , B , C , and D are mutually exclusive and exhaustive events, P(A) + P(B) + P(C) + P(D) = 1 2k + 3k + 5k + 8k = 1 18k = 1 k = 1 18 We need to evaluate 2P(A) + 3P(B) 4P(C) + 5P(D) Substituting the values in terms of k : 2(2k) + 3(3k) 4(5k) + 5(8k) = 4k + 9k 20k + 40k = 13k 60k = 13 60 Answer: 13 60

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