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 $33,000 on a clear day and $15,000 on a cloudy day. They will make a loss of $7,000 if it rains. The weather channel has predicted a 52% chance of rain on the day of the concert. Calculate the expected profit from the concert of the likelihood is 11% that it will be sunny and 37% that it will be cloudy.

Expected profit refers to the estimated profit that is likely to be received from a transaction. It is calculated as a product of the probability of receiving a profit to the profit.

The expected profit for events A, B, and C can be calculated as:

[tex]\rm Expected\: Profit = [A\times P(A)] +[B\times P(B)]+[C\times P(C)][/tex]

where A, B, and C are the profits and P(A), P(B), and P(C) is the probability of events A, B, and C respectively.

Given:

Profit on a clear day is $33,000

The probability of a clear day is 11%

Profit on a cloudy day is $15,000

The probability of a cloudy day is 37%

Loss on a rainy day is $7,000

The probability of a rainy day is 52%

Therefore the expected profit will be:

[tex]\rm Expected\: Profit = [33,000\times 0.11] +[15,000\times 0.37]-[7,000\times 0.52]\\\\\rm Expected\: Profit = [3,630] +[5.550]-[3,640]\\\rm Expected\: Profit = \$5,540[/tex]

The loss on a rainy day is subtracted to calculate the expected profit.

Therefore the expected profit is $5,540.

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