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Two independent events A and B are such that P(A B)= 2 3 and P ( A B )= 1 6 . If P ( B ) P ( A ) , then what is P ( B ) equal to ?

Options

  1. A1 4
  2. B1 3
  3. C1 2
  4. D1 6

Correct answer

B. 1 3

Step-by-step solution

P(A B)= 2 3 P(A B)= 1 6 Since, A and B are independent events, P(A B)=P(A) P(B)= 1 6 ...(1) aligned & P(A B)= 2 3 P(A)+P(B)-P(A B)= 2 3 & P(A)+P(B)- 1 6 = 2 3 aligned P(A)+P(B)= 2 3 + 1 6 = 5 6 ...(2) aligned & from (1), (2), P ( B )= 1 3 or 1 2 & P(B) P(A), P(B)= 1 3 aligned

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