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If A and B are independent events such that P ( A )= 1 5 , P ( A B )= 7 10 , then what is P ( B ) equal to?

Options

  1. A2 7
  2. B3 7
  3. C3 8
  4. D7 9

Correct answer

C. 3 8

Step-by-step solution

As A and B are independent events, so P ( ~A ~B )= P ( ~A ) . P ( ~B ) Now, from aligned P ( ~A ~B ) & = P ( ~A )+ P ( ~B )- P ( ~A ~B ) 7 10 & = 1 5 + P ( ~B )- 1 5 P ( ~B ) aligned or, 1 2 = 4 5 P ( B ) P ( B )= 5 8 P ( B )=1- P ( B )= 3 8

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