An outdoor concert featuring a popular musical group is scheduled for a Sunday a
ID: 3207208 • Letter: 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.
Probability Get Insurance No Insurance Rain 0.24 90,000 10,000 No Rain 0.76 80,000 100,000