Question

Question #7d4be

Answer 1

`.5795`

Explanation:

Let `B` be the event of raining and `A` be the event that the theater is full

we are asked for `p(A)`, the probability of the theater being full.
we are given the following
`p(A|B) = .8` The probability of being full given it rains
`p(A|notB) = .45` The probability of being full given it does not rain aka sunny day
`p(B) = .37` The probability of raining

Based on the law of total probability we know that
`p(A) = p(A,B)+p(A,notB) =`
`p(A|B)p(B)+p(A|notB)p(notB)`

now we just plug in
`p(A) =.8*.37+.45*.63= .5795`