Learning statisticts and probability

[slug]

I saw this problem in a book review, but it doesn't give an answer

If there is a 75% chance I will go out and eat dinner at a restaurant on Friday night and there is 45% chance I will go see a movie on friday night
then what is the probability that I see a movie and eat dinner at a restaurant?

At first my stupid intuition told me to just add 75 and 45 and divide by 200
which would be 120/200 = .6 = 60% (.75+.45)/2

But then I realized that the combined chances had to be less than 45%.
So i just multiplied 45*0.75 = 33.75% or 75*.45 = 33.75%
33.75 seems correct to me although the logic is weird
is this the right answer and is there another way of finding the solution

also are there any good books you could recommend for learning statisticts and probability

 

[matt grime]

Depends if you consider them to be independent events or not, otherwise knowing the probability of A and the probability of B doesn't tell you anything about the probability of A and B occurring.

If they are independent then, yes, you just multiply them together.

 

[kleinwolf]

Could we also understand : I go to the restaurant or to the movie with certainty (I cannot choose neither of them) :

p(movie or dinner)=1=p(movie)+p(diner)-p(movie and diner)

Implying : p(movie and diner)=.75+.45-1=.2=20% ??

 

[Data]

Yes, that's fine. The events are not independent in that case.