Probability proof clarification 2

Question

Suppose that A and B are two events such that $$P(A) =.8$$ $$P(B) =.7$$

Is it possible that

a) $$P(A\cup B)=.5$$ and that

b)$$P(A \cap B) =.75?$$

Since there is no information on the sets relationships, is it wrong to say that a) "it's possible" and b) "not possible"

... because we know that the lowest it can be is zero and highest value it can be is .7

Answer 1

Hints

Since $A\subset A\cup B$ it is $P(A)\le P(A\cup B).$

Since $A\cap B\subset B$ it is $P(A\cap B)\le P(B).$

Answer 2

No. This is because if $C\subseteq D$, then $P(C)\leq P(D)$.

And, of course, because $A\cap B\subseteq B$ and $A\subseteq A\cup B$.