If P(A) = 0.4, P(B | A) = 0.35, P(A $\cup$ B) = 0.69, then P(B) =
A)0.14
B)0.43
C)0.75
D)0.59

Question

Quizplus · Accepted Answer

Using the law of total probability: P(A F1F1F1S1F1F1F10 B) = P(B | A) * P(A) + P(B | A^c) * P(A^c) Where A^c represents the complement of event A. We can rearrange and solve for P(B): P(B) = [P(A F1F1F1S1F1F1F10 B) - P(B | A^c) * (1 - P(A))] / P(A) Substituting the given values: P(B) = [0.69 - P(B | A^c) * 0.6] / 0.4 We don't have enough information to directly solve for P(B | A^c), but we can use the fact that P(B) must be between 0 and 1: 0 < P(B) < 1 0 < [0.69 - P(B | A^c) * 0.6] / 0.4 < 1 0 < 1.725 - 1.5P(B | A^c) < 2.5 -1.725 < -1.5P(B | A^c) < 0.775 1.15 > P(B | A^c) > -0.517 Since probabilities must be between 0 and 1, we can conclude that: 0.35 < P(B) < 1 Eliminating the impossible lower bound, we get: 0.43 < P(B) < 1 The only answer choice within this range is B, 0.43.

If P(A) = 0 ∪\cup∪ B) = 069, Then P(B) = A)0

If P(A) = 0 $\cup$ B) = 069, Then P(B) =
A)0