Need help with a probability quesiton

Question

Jeff is producing an outdoor concert. He estimates that he will make 3900 dollars if it does not rain, and make 850 dollars if it does rain. The local weather station (which we'll assume is accurate in giving forecasts) predicts that the chance of rain is 13 percent for the day of the concert. What is Jeff's expected earnings from the concert?

Answer 1

 

Hi Lauren,

In order to come up with the expected earning,

we, first, need to calculate the expected earning for each event/case and

then simply to sum them up over all possible events/cases.

In this specific problem,

we have two possible events/cases:

1) if it rains on the day of concert, and

2) if it does not.

In case of 1), assuming it rains (of which chance is 13%)

the estimated earning is $850.

So, the expected earning is

$850 × 0.13 = $110.5

In case of 2), assuming it does not rain (of which chance is 87%)

the estimated earning is $3,900.

So, the expected earning is

$3,900 × 0.87 = $3,393

Summing up two expected earnings,

Jeff's expected earning from the concert is

$3,503.5 (= $110.5 + $3,393)

Hope this helps.