Please help me with a proof!?

Question

Can anyone tell me how to prove that :
P(A)+P(B)-1 <= P(A intersect B)

Answer 1

Switch this so it says P(A)+P(B)-P(A int. B)<=1.

The left side of the equation is equivalent to A union B, which has a maximal probability of 1.

Answer 2

You know that:

P(A union B) <= 1

You also know that:

P( A union B ) = P(A) + P(B) - P(A intersect B)

Thus,

P(A) + P(B) - P(A intersect B) <= 1

Add P(A intersect B) to both sides and subtract 1 from both sides. The result:

P(A) + P(B) - 1 <= P(A intersect B)