aryannn_1712 wrote:
If the probability is 0.7 that event X will occur and 0.85 that event Y will occur, what is the least possible value of the probability that both events will occur? (A) 0.15 (B) 0.55 (C) 0.595 (D) 0.7 (E) 0.85
B: 0.55.
P(X) = 0.7
B(Y) = 0.85
P(X and Y) = P(X) + P(Y) - P(X or Y)
P(X and Y) = 0.7 + 0.85 - P(X or Y)
P(X and Y) = 1.55 - P(X or Y)
Now, we know that probability can not be less than 0, and can not be more than 1. Thus, to minimize P(X and Y) we need to maximize P(X or Y). P(X or Y) can be set as much as 1. And thus,
P(X and Y) = 1.55 - 1 = 0.55.
Hence, (B) 0.55 is the answer.