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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- May 1st 2008, 01:30 PMccdelia7Events 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. - May 1st 2008, 01:33 PMIsomorphism
- May 1st 2008, 01:42 PMPlato
$\displaystyle 1 \ge P(A \cup B) = P(A) + P(B) - P(A \cap B) > \left( {1/2} \right) + \left( {1/2} \right) - P(A \cap B)$

Can you use that to finish? - May 1st 2008, 01:55 PMccdelia7
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 - May 1st 2008, 02:04 PMIsomorphism
(Headbang)(Wondering) I dont understand what you are saying

But**Plato**nearly answered your question

$\displaystyle 1 \ge P(A \cup B) = P(A) + P(B) - P(A \cap B) > \left( {1/2} \right) + \left( {1/2} \right) - P(A \cap B) \Rightarrow 0 < P(A \cap B)$

Thus we see it is greater than 0. So it cannot be 0 :)