"Jay, a writer of novels, just has completed a new thriller novel. A movie company and a TV network both want exclusive rights to market his new title. If he signs with the network, he will receive a single lump sum of $1,460,000, but if he signs with the movie company, the amount he will receive depends on how successful the movie is at the box office.The probability of a small box office earning $210,000 is 0.27. The probability of a medium box office of $1,530,000 is 0.64, and the probability of a large box office of $3,190,000 is 0.09.Jay can send his novel to a prominent movie critic to assess the potential box office success. It will cost $21,000 to get the novel evaluated by the movie critic.The movie critic can have either a favorable or unfavorable opinion. The movie critic's reliability of predicting box office success is as follows.If the movie will have a large box office, there is a 0.61 probability the critic will have a favorable opinion.If the movie will have a medium box office, there is a 0.44 probability the critic will have a favorable opinion.If the movie will have a small box office, there is a 0.09 probability the critic will have a favorable opinion.Assume that Jay wants to maximize his expected monetary outcome. Enter the expected value of the preferred alternative. This includes whether or not to hire the movie critic and whether or not to go with the movie or network option."

Question
Asked Dec 7, 2019
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"Jay, a writer of novels, just has completed a new thriller novel. A movie company and a TV network both want exclusive rights to market his new title. If he signs with the network, he will receive a single lump sum of $1,460,000, but if he signs with the movie company, the amount he will receive depends on how successful the movie is at the box office.
The probability of a small box office earning $210,000 is 0.27. The probability of a medium box office of $1,530,000 is 0.64, and the probability of a large box office of $3,190,000 is 0.09.
Jay can send his novel to a prominent movie critic to assess the potential box office success. It will cost $21,000 to get the novel evaluated by the movie critic.
The movie critic can have either a favorable or unfavorable opinion. The movie critic's reliability of predicting box office success is as follows.
If the movie will have a large box office, there is a 0.61 probability the critic will have a favorable opinion.
If the movie will have a medium box office, there is a 0.44 probability the critic will have a favorable opinion.
If the movie will have a small box office, there is a 0.09 probability the critic will have a favorable opinion.
Assume that Jay wants to maximize his expected monetary outcome. Enter the expected value of the preferred alternative. This includes whether or not to hire the movie critic and whether or not to go with the movie or network option."

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Expert Answer

Step 1

Small Box-Office Earning:

The probability of small box-office earning = 0.27

Earnings = $210,000

Probability of favorable critic opinion = 0.61

Medium Box-Office Earning:

The probability of medium box-office earning = 0.64

Earnings = $1,530,000

Probability of favorable critic opinion = 0.44

Large Box-Office Earning:

The probability of large box-office earning = 0.09

Earnings = $3,190,000

Probability of favorable critic opinion = 0.09

Cost of sending to the critic = 21,000

Step 2

Case 1: Movie critic is hired and signed with the company:

Earnings = 0.27 × 210,000 × 0.61 + 0.64 × 1,530,000 × 0.44 + 0.09 × 3,190,000 × 0.09 – 21,000

               = 36,288 + 430,848 + 25,839 – 21,000

               = 471,975

Case 2: Signed with the company ...

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