Prove the following statements about any probability functio

Prove the following statements about any probability function P and any sets A and B:

Solution

a)

we have P(A) + P(B) - P(A and B ) = P(A or B)

P(A) always be lower than 1 because the sum of all probabilities in a sample space will be 1

for example if we have 2 events the sum of both events will be always 1

so P(A) never will be greater than 1

b)

P(A and B) = P(A) + P(B) - P(A or B)

P(A and B) will be lower than the min. of probabilities because

P(A and B) depends of P(A) and P(B) , and P(A and B) is the intersection of both events