SOLUTION: Suppose that A and B are two events such that P(A) + P(B) > 1. a. What is the smallest possible value for P(A intersection B)? b. What is the largest possible value for P(A

Algebra ->  Probability-and-statistics -> SOLUTION: Suppose that A and B are two events such that P(A) + P(B) > 1. a. What is the smallest possible value for P(A intersection B)? b. What is the largest possible value for P(A      Log On


   

Question 1123479: Suppose that A and B are two events such that P(A) + P(B) > 1.
a. What is the smallest possible value for P(A intersection B)?
b. What is the largest possible value for P(A intersection B)?
Answer by greenestamps(13200) About Me  (Show Source):
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a. There is no smallest possible value for P(A intersection B).

If P(A)+P(B) were EQUAL to 1, instead of greater than 1, then the smallest possible value for P(A intersection B) would be 0.

But if P(A)+P(B) is GREATER THAN 1, then P(A intersection B) has to be a positive number.

But there is no smallest positive number.

b. 1. If P(A) = P(B) = 1, then P(A intersection B) is 1.