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Math Help - Events and Sample space

  1. #1
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    Smile Events and Sample space

    Suppose that A & B are events in a sample space and that P(A) > (1/2) and P(B) > (1/2).

    Prove that P(A "intersection" B) does not equal 0.
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  2. #2
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    Quote Originally Posted by ccdelia7 View Post
    Suppose that A & B are events in a sample space and that P(A) > (1/2) and P(B) > (1/2).

    Prove that P(A "intersection" B) does not equal 0.
    Hint: P(A \cup B)  = P(A) + P(B) - P(A \cap B) and P(A \cup B) \leq 1
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  3. #3
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    1 \ge P(A \cup B) = P(A) + P(B) - P(A \cap B) > \left( {1/2} \right) + \left( {1/2} \right) - P(A \cap B)

    Can you use that to finish?
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  4. #4
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    Smile

    similar to:

    limit as n approaches zero, we know that P( A intersection B) must be greater than zero, though it may be close ( as the aforementioned limit). And thus, we see that it also cannot equal zero!

    I think I may have been a bit vague, but let me know if that sounds right.

    I think I have the right approach now.

    Thanks
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  5. #5
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    Quote Originally Posted by ccdelia7 View Post
    similar to:

    limit as n approaches zero, we know that P( A intersection B) must be greater than zero, though it may be close ( as the aforementioned limit). And thus, we see that it also cannot equal zero!

    I think I may have been a bit vague, but let me know if that sounds right.

    I think I have the right approach now.

    Thanks
    I dont understand what you are saying

    But Plato nearly answered your question
    1 \ge P(A \cup B) = P(A) + P(B) - P(A \cap B) > \left( {1/2} \right) + \left( {1/2} \right) - P(A \cap B) \Rightarrow 0 < P(A \cap B)
    Thus we see it is greater than 0. So it cannot be 0
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