Question #7d4be

1 Answer
Will
Aug 8, 2016

.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∣¬B)=.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,¬B)=
p(A∣B)p(B)+p(A∣¬B)p(¬B)

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

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