An outdoor concert featuring a popular musical group is scheduled for a Sunday a

Question

An outdoor concert featuring a popular musical group is scheduled for a Sunday afternoon in a large open stadium. The promoter, worrying about being rained out, contacts a long-range weather forecaster who predicts the chance to rain on that Sunday to be 0.24. If it does not rain, the promoter is certain to net $100,000; if it does rain, the promoter estimates that the net will be only $10,000. An insurance company agrees to insure the concert for $100,000 against rain at a premium of $20,000. Should the promoter buy the insurance and why?

Please explain.

Explanation / Answer

If they insure & it rains,

they will get =100,000 – premium + net amount due to rain

=100,000-20,000+10,000

=90,000

Expected value if Insurance taken

E(X)= 90,000*0.24 + 80,000*0.76

E(X)=$82,400

Expected value if Insurance not taken

E(X)= 10,000*0.24 + 100,000*0.76

E(X)=$78,400

As the Expected value is greater after Insurance, So promoter should buy the insurance.

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