Suppose P(A) = 0.4 , P(B) = P , and P(A B) = 0.7 . If A and B are independent events, then the value of P is: - Mathematics MCQ Mathematics Mock Test - 1 2026 | ExamTest.live

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Suppose P (A) = 0.4, P (B) = P, and P (A \cup B) = 0.7 . If A and B are independent events, then the value of P is:

Solution & Step-by-step Explanation

For any two events A and B : P (A \cup B) = P (A) + P (B) - P (A \cap B) Since A and B are independent events, P (A \cap B) = P (A) \times P (B) .Substituting the values: 0.7 = 0.4 + P - (0.4 \times P) 0.7 - 0.4 = P - 0.4 P 0.3 = 0.6 P P = \frac{0.3}{0.6} = 0.5

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Suppose P (A) = 0.4, P (B) = P, and P (A \cup B) = 0.7 . If A and B are independent events, then the value of P is:

0.5

0.3

0.55

0.6

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