Use the following to answer question:
-(Table: Natasha's Total Utility)Use Table: Natasha's Total Utility.Natasha earns $50,000 per year but faces losing $20,000 of it if she is late with her work.If there is a 25% probability that Natasha will be late with her work and her income will equal $30,000,the premium for a fair insurance policy to eliminate the uncertainty in her income would equal:
A)$4,000.
B)$5,000.
C)$7,500.
D)$9,500.

Question

Use the following to answer question: 
-(Table: Natasha's Total Utility)Use Table: Natasha's Total Utility.Natasha earns $50,000 per year but faces losing $20,000 of it if she is late with her work.If there is a 25% probability that Natasha will be late with her work and her income will equal $30,000,the premium for a fair insurance policy to eliminate the uncertainty in her income would equal:
A)$4,000. 
B)$5,000. 
C)$7,500. 
D)$9,500.

Quizplus · Accepted Answer

The expected value of Natasha's income can be calculated as follows:

Expected Value = (Probability of being on time x Income if on time) + (Probability of being late x Income if late)

Expected Value = (0.75 x $50,000) + (0.25 x $30,000)

Expected Value = $45,000

Since Natasha is facing a potential loss of $20,000, the fair premium for insurance would be equal to the expected loss:

Fair Premium = Probability of loss x Amount of loss

Fair Premium = 0.25 x $20,000

Fair Premium = $5,000

Therefore, the correct answer is B.

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