If two events A and B have probabilities as P(A) = 0.45 and P(B) = 0.7, then what is the smallest possible value for P(A and B)?
A) 0.1
B) 0.15
C) 0.3
D) 0.35

Question

Quizplus · Accepted Answer

The smallest possible value for P(A and B) occurs when the intersection of A and B is as small as possible, given the constraints of their individual probabilities. The formula for the intersection of two events is P(A and B) = P(A) + P(B) - P(A or B). Since P(A or B) cannot exceed 1, the smallest P(A and B) can be is P(A) + P(B) - 1 = 0.45 + 0.7 - 1 = 0.15.

If Two Events a and B Have Probabilities as P(A)