Question

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 $40,000 on a clear day and $14,000 on a cloudy day. They will make a loss of $5,000 if it rains. The weather channel has predicted a 60% 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 26% that it will be cloudy.

Answer 1

$6240

Explanation:

given likelihoods:

sunny day = 14% = 0.14

cloudy day = 26% = 0.26

rainy day = 60% = 0.60

profits:

profit on a sunny day = $40,000

profit on a cloudy day = $14,000

Loss on a rainy day = -$5,000

expected profit = (probability of sunny day * profit on sunny day) + (probability of cloudy day * profit on cloudy day) + (probability of rainy day * loss on rainy)

expected profit = (0.14 * $40,000) + (0.26 * $14,000) + (0.60 * -$5,000)

=6240