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For two events A and B , it is given that the probabilities of both occurring, only A occurring, and only B occurring are in the ratio P(A B) : P(A B') : P(A' B) = 2 : 3 : 4 . If the probability that at least one of the events occurs is 9 10 , then the conditional probability P(A|B') is equal to

Options

  1. A3 4
  2. B2 3
  3. C3 5
  4. D1 3

Correct answer

A. 3 4

Step-by-step solution

Let the probabilities be P(A B) = 2x , P(A B') = 3x , and P(A' B) = 4x . The probability that at least one of the events occurs is P(A B) . Since the sets (A B) , (A B') , and (A' B) are mutually exclusive and their union is A B , we have: P(A B) = P(A B) + P(A B') + P(A' B) 9 10 = 2x + 3x + 4x 9 10 = 9x x = 1 10 From this, we can determine the individual probabilities: P(A B') = 3x = 3 10 The probability of event B occurring is: P(B) = P(A B) + P(A' B) = 2x + 4x = 6x = 6 10 The probability of event B not occurring

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