Probability Proof

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• June 30th 2010, 04:49 PM
teramaries
Probability Proof
Suppose A and B are events in a sample space and that P(A) >1/2 and P(B) >1/2. Prove that P(A intersect B) does not = 0
• June 30th 2010, 05:46 PM
mr fantastic
Quote:

Originally Posted by teramaries
Suppose A and B are events in a sample space and that P(A) >1/2 and P(B) >1/2. Prove that P(A intersect B) does not = 0

Recall that $\Pr(A \cap B) = \Pr(A) + \Pr(B) - \Pr(A \cap B)$. Is $\Pr(A \cup B) > 1$ possible? Therefore, what do you conclude?