ProbabilityHard
Question
Two events A and B have probabilities 0.25 and 0.50 respectively. The probabilitity that both A and B occur simultaneoushly is 0.14 Then, the probability that neither A nor B occurs is
Options
A.0.39
B.0.25
C.0.11
D.None of these
Solution
Given, P(A) = 0.25, P(B) = 0.50, P(A ∩ B) = 0.14
∴ P(A ∪ B) = P(A) + P(B) - P(A ∩ B)
⇒ P(A ∪ B) = 0.25 + 0.50 - 0.14
P(A ∪ B) = 0.61
∴ P(A ∪ B) = 1 - P(A ∩ B) = 1 - 0.61 = 0.39
∴ P(A ∪ B) = P(A) + P(B) - P(A ∩ B)
⇒ P(A ∪ B) = 0.25 + 0.50 - 0.14
P(A ∪ B) = 0.61
∴ P(A ∪ B) = 1 - P(A ∩ B) = 1 - 0.61 = 0.39
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