Use the following to answer question:
-(Table: Choice with Uncertainty)Use Table: Choice with Uncertainty.Suppose that the probability that the sitcom does not make it to television is 30%,that it makes it to television but is not the most viewed show in its time slot is 50%,and that it makes it to television and is the most viewed show in its time slot is 20%.Given this information,Norman's expected income is:
A)$52,500.
B)$47,500.
C)$40,000.
D)$37,500.

Question

Use the following to answer question: 
-(Table: Choice with Uncertainty)Use Table: Choice with Uncertainty.Suppose that the probability that the sitcom does not make it to television is 30%,that it makes it to television but is not the most viewed show in its time slot is 50%,and that it makes it to television and is the most viewed show in its time slot is 20%.Given this information,Norman's expected income is:
A)$52,500. 
B)$47,500. 
C)$40,000. 
D)$37,500.

Quizplus · Accepted Answer

To calculate expected income, we need to multiply the payoff for each possible outcome by its probability of occurring, and then add up these products. 
Expected income = (0.3 x $0) + (0.5 x $50,000) + (0.2 x $100,000) = $0 + $25,000 + $20,000 = $45,000. 
However, there is an option to pay $2,500 for a market research report that will provide additional information about the likelihood of success. If Norman buys the report and decides not to air the sitcom, he will lose the $2,500. But if he airs it, the probabilities and payoffs will change based on the information in the report:
- If the report says there is an 80% chance of success, the probabilities become: 20% success, 80% failure. The payoffs remain the same. 
- If the report says there is a 20% chance of success, the probabilities become: 0% success, 100% failure. The payoffs remain the same. 
Calculating the expected values with the report:
- If Norman airs the sitcom without buying the report, his expected income is $45,000. 
- If he buys the report:
     - If the report says there is an 80% chance of success, his expected income becomes: (0.2 x $100,000) + (0.8 x -$2,500) = $20,000 - $2,000 = $18,000. 
     - If the report says there is a 20% chance of success, his expected income becomes: (0 x $100,000) + (1 x -$2,500) = -$2,500. 
Therefore, the best choice is to buy the report and air the sitcom if the report suggests there is an 80% chance of success, which gives an expected income of $52,500 ($50,000 for airing the sitcom plus $2,500 for the report).

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