In: Statistics and Probability
"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 $980,000, 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 $295,000 is 0.25. The
probability of a medium box office of $1,210,000 is 0.49, and the
probability of a large box office of $3,180,000 is 0.26.
Jay can send his novel to a prominent movie critic to assess the
potential box office success. It will cost $24,000 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 0.63
probability the critic will have a favorable opinion.
If the movie will have a medium box office, there is a 0.41
probability the critic will have a favorable opinion.
If the movie will have a small box office, there is a 0.11
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."
Hence we can conclude that Jay can maximize his profit by not hiring a critic and signing with movie company. In this case the expected profit $1,493,450.