Question

The probability a resident of Manhattan spends New Years Eve at Times Square is 0.32. The probability a resident of Manhattan spends New Years Eve out of town is 0.22. Assume a Manhattan resident spending New Years Eve at Times Square is mutually exclusive of the resident spending New Years Eve out of town.

What is the probability a randomly selected Manhattan resident is out of town on New Years Eve given the resident spends New Years Eve at Times Square?

Group of answer choices

0.22

0.1

0.32

0

0.688

Answer 1

let, the events be:-

A :  a resident of Manhattan spends New Years Eve at Times Square

B :  a resident of Manhattan spends New Years Eve out of town

given probabilities are:-

P(A) = 0.32

P(B) = 0.22

we have assumed that a Manhattan resident spending New Years Eve at Times Square is mutually exclusive of the resident spending New Years Eve out of town.

so, A and B are mutually exclusive events.

if two events are mutually exclusive, then,

the probability a randomly selected Manhattan resident is out of town on New Years Eve given the resident spends New Years Eve at Times Square be;-

[ as A and B are mutually exclusive events]

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