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expected value

Sampling Fruit A merchant buys boxes of fruit from a grower and sells them. Each box of fruit is either Good or Bad. A Good box contains 80% excellent fruit and will earn $200 profit on the retail market. A Bad box contains 30% excellent fruit and will produce a loss of $1000. The a priori probability of receiving a Good box of fruit is .9.
Before the merchant decides to put the box on the market, he can sample one piece of fruit to test whether it is excellent. Based on that sample, he has the option of rejecting the box without paying for it. Determine the expected value of the right to sample. (Hint: If the merchant samples the fruit, what are the probabilities of accepting a Good box, accepting a Bad box, and not accepting the box? What are these probabilities if he does not sample the fruit?)

a.0 b. $16 c. $34 d. $72 e. $80

Solution Preview

Hello,

Here you are asked to determine the expected value (in $) the right to sample.

To get started, let's first determine the three probabilities listed in the hint:
1). P(accepting a good box with sampling): To accept a good box, the merchant has to both receive a good box AND sample an excellent fruit given that he got a good box. SO,
P(accepting a good box)= P(gets a good box)*P(sample excellent fruit) = 0.9*0.8 = 0.72

2). P(accepting a bad box with sampling): To accept a bad ...

Solution Summary

Ddetermine the expected value (in $) the right to sample.

$2.19