
de Morgan's law
I need help. I just can't figure out where to go with this one..
For two events A and B show that:
P(A intersection B) is greater than or equal to P(A) + P(B)  1
Hint: Apply de Morgan's law and then the Bonferroni inequality.
(I don't know how to type the symbols out, so I used words instead)
Help is greatly appreciated... Extra 'bubbly' all around..


Hi
The De Morgan's law is:P(AUB) = P(A) + P(B)  P(A intersection B)
And we know that P(AUB) <= 1
Implies: P(AUB) = P(A) + P(B)  P(A intersection B) <= 1
Implies: P(A) + P(B)  P(A intersection B) <= 1
Implies: P(A) + P(B)  P(A intersection B)  1 <= 1  1
Implies: P(A) + P(B)  P(A intersection B)  1 <= 0
Implies: P(A) + P(B)  1 <= P(A intersection B)
Thus,
P(A intersection B) >= P(A) + P(B)  1.

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