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Organizers of an outdoor summer concert in Toronto are concerned about the weather conditions on the day of the concert. They will make a profit of $31,000 on a clear day and $10,000 on a cloudy day. They will make a loss of $5,000 if it rains. The weather channel has predicted a 47% chance of rain on the day of the concert. Calculate the expected profit from the concert if the likelihood is 14% that it will be sunny and 39% that it will be cloudy.

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Answer: Expected profit is $5,750

Step-by-step explanation:

Given data:

Profit on clear day = $30,000

Profit on a cloudy day = $10,000

Loss when it rains = $5,000

Likelihood = 14%

Sunny = 39%

Solution

First we apply the Expected profit formula

= (30,000*0.14)+(10,000*0.39)+(-5000*0.47)

= $4200 + $3900 + ($2350)

= $8100 + ($2350)

= $5,750

The calculated expected profit is $5,750.

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