The Student Room Group

P(A n B) <(=) min{P(A), P(B)}

The questions says:

"Show that, for any two events A and B,

P(AB)min P( A \cap B) \leq min {P(A),P(B)P(A),P(B)}


What does this mean?

What am I looking to prove?

Is it that P(A n B) is less than or equal to the minimum value in the set from P(A) to P(B)? If it is, how do I do this?

Thanks :smile:
Reply 1
Well, I hope it's obvious that P(AB)P(A)\mathbb{P}(A \cap B) \le \mathbb{P}(A) and P(AB)P(B)\mathbb{P}(A \cap B) \le \mathbb{P}(B). So then it must be smaller than the smallest of the two of them. And that's exactly what you wanted to show.

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