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 $36,000 on a clear day and $17,000 on a cloudy day. They will make a loss of $5,000 if it rains. The weather channel has predicted a 48% chance of rain on the day of the concert. Calculate the expected profit from the concert if the likelihood is 13% that it will be sunny and 39% that it will be cloudy. Do not include the $ sign when you type your answer. (Blackboard can't understand it.)

Question

Mathematics

Sonny Shepard

2 November, 21:51

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 $36,000 on a clear day and $17,000 on a cloudy day. They will make a loss of $5,000 if it rains. The weather channel has predicted a 48% chance of rain on the day of the concert. Calculate the expected profit from the concert if the likelihood is 13% that it will be sunny and 39% that it will be cloudy. Do not include the $ sign when you type your answer. (Blackboard can't understand it.)

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Cullen · Answer 1

The value of the expected profit from the concert is 8,910

Step-by-step explanation:

Profit on a clear day X₁ = 36,000 with 13% probability.

i. e X₁ = 36000

P (X₁) = 0.13

Profit on a cloudy day = 17,000 with 39% probability.

i. e X₂ = 17000

P (X₂) = 0.39

else,

loss of 5,000 if it rains with the probability of 48%.

i. e X₃ = 5000

P (X₃) = 0.48

The value of the expected profit from the concert is obtained as follows

Expected Value = (36,000*0.13) + (17,000*0.39) - (5,000*0.48)

= 4,680 + 6,630 - 2,400

= 8,910