Jose Morales manages a large outdoor fruit stand in one of the less affluent neighborhoods of San Jose, California. To r
Posted: Wed Apr 06, 2022 9:09 am
Jose Morales manages a large outdoor fruit stand in one of the
less affluent neighborhoods of San Jose, California.
To replenish his supply, Jose buys boxes of fruit early each
morning from a grower south of San Jose. About 90 percent of the
boxes of fruit turn out to be of satisfactory quality, but the
other 10 percent are unsatisfactory. A satisfactory box contains 80
percent excellent fruit and will earn $200 profit for Jose. An
unsatisfactory box contains 30 percent excellent
fruit and will produce a loss of $1,000. Before Jose decides to
accept a box, he is given the opportunity to sample one piece of
fruit to test whether it is excellent. Based on that sample,
he then has the option of rejecting the box without paying for it.
Jose wonders (1) whether he should continue buying from this
grower, (2) if so, whether it is worthwhile sampling just one piece
of fruit from a box, and (3) if so, whether he should be accepting
or rejecting the box based on the outcome of this sampling.
Use the likelihoods/conditional and prior probabilities to
calculate all the posteriors/revised probabilities. Show your
work/calculations. (6 points) N.B.: Round the probabilities to two
decimal points.
b) Draw and solve the decision tree for this problem to determine
the optimal decision strategy that Jose should follow. (Show your
work/calculations). Verbally communicate the decision strategy. (25
points)
less affluent neighborhoods of San Jose, California.
To replenish his supply, Jose buys boxes of fruit early each
morning from a grower south of San Jose. About 90 percent of the
boxes of fruit turn out to be of satisfactory quality, but the
other 10 percent are unsatisfactory. A satisfactory box contains 80
percent excellent fruit and will earn $200 profit for Jose. An
unsatisfactory box contains 30 percent excellent
fruit and will produce a loss of $1,000. Before Jose decides to
accept a box, he is given the opportunity to sample one piece of
fruit to test whether it is excellent. Based on that sample,
he then has the option of rejecting the box without paying for it.
Jose wonders (1) whether he should continue buying from this
grower, (2) if so, whether it is worthwhile sampling just one piece
of fruit from a box, and (3) if so, whether he should be accepting
or rejecting the box based on the outcome of this sampling.
Use the likelihoods/conditional and prior probabilities to
calculate all the posteriors/revised probabilities. Show your
work/calculations. (6 points) N.B.: Round the probabilities to two
decimal points.
b) Draw and solve the decision tree for this problem to determine
the optimal decision strategy that Jose should follow. (Show your
work/calculations). Verbally communicate the decision strategy. (25
points)