Show using the axioms for probability laws and what we have

Show, using the axioms for probability laws and what we have learned about set theory, that the following are true: You can use Venn diagrams to illustrate your argument, but students who only use Venn diagrams will not receive full credit.

Solution

a)

P(A) > P(A intercept B)

that is because when the events have a success in common P(A intercept B) is only the common part of the 2 events, while P(A) is whole event

P(A) < P(A U B)

that is because the union of these events is a sum that subctrat the common part because P(A)+P(B) you are taking P(A intercept B) twice, so we need to subctract one time P(A intercept B) so P(A) is always lower than

P(A U B)