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A rock concert promoter has scheduled an outdoor concert on July 4th. If it does not rain, the promoter will make $30,000. If it does rain, the promoter will lose $15,000 in guarantees made to the band and other expenses. The probability of rain on the 4th is 0.4.

(a) What is the promoter's expected profit? Is the expected profit a reasonable decision criterion? (Round your answers to 1 decimal place.)
(b) How much should an insurance company charge to insure the promoter's full losses?

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pedrocarratore

Answer:

(a) $12,000. It is reasonable since profit is positive

(b) $6,000

Step-by-step explanation:

(a) The promoter's expected profit is given by the product of his potential earnings by the probability that it does not rain, minus the product of his potential losses by the probability of rain:

[tex]E(X) = \$30,000*(1-0.4)-\$15,000 *0.4\\E(X) = \$12,000[/tex]

The promoter's expected profit is $12,000, it is a reasonable criterion since profit is positive.

(b) An insurance company should charge the product of the full potential losses by the probability of rain:

[tex]I = \$15,000*0.4\\I=\$6,000[/tex]

An insurance company should charge $6,000.

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