I'm studying Introduction to probability and currently, I'm stuck with the following problem. Given:
$P(A)=0.7$, $P(B)=0.5$, $P(A\cap B)=0.45$
What is the probability of A and not B?
I've checked this similar question but I don't understand the answers. Also I've asked my instructor and she told me that $1-P(A\cap B)(P(B^c))$ is the answer (As the answers suggested, this result is not correct). Why is that? She does not provided me a completely explanation.
Update 1: The original problem is the following
In a multiplex cinema, there are two different rooms, $A$ and $B$, working simultaneously. Let $SA$ be the event that, during a certain showing, room $A$ becomes full before the film begins, and let $SB$ be the event that, during the same showing, room $B$ becomes full before the beginning of the movie. We know that $P(SA)=0.7$; $P(SB)=0.5$ and $P(SA∩SB)=0.45$
Calculate the probability that room $A$ will become full and room $B$ will not.
Did I state the problem correctly?