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1. Assume Mike Trout has the following distribution of outcomes for 2012. If he

ID: 3152623 • Letter: 1

Question

1.     Assume Mike Trout has the following distribution of outcomes for 2012. If he gets hurt, he will need some time to recover even while in the lineup, so he cannot produce at his highest level even if he comes back from an injury. If he does not get hurt, then he is certain to either Produce A, B or C, with A > B > C.

Outcome

Probability

Return/Production

Gets Hurt, Misses Whole Season

10%

0 wins

Gets Hurt, Misses 1/2 season, Produces B

20%

1.5 wins

Gets Hurt, Misses 1/2 season, Produces C

10%

0.75 wins

Gets Hurt, Misses 1/4 season, Produces B

10%

3 wins

Gets Hurt, Misses 1/4 season, Produces C

10%

1.5 wins

No Injury, Produces A

20%

10 wins

No Injury, Produces B

10%

6 wins

No Injury, Produces C

10%

3 wins

Outcome

Probability

Return/Production

Gets Hurt, Misses Whole Season

10%

0 wins

Gets Hurt, Misses 1/2 season, Produces B

20%

1.5 wins

Gets Hurt, Misses 1/2 season, Produces C

10%

0.75 wins

Gets Hurt, Misses 1/4 season, Produces B

10%

3 wins

Gets Hurt, Misses 1/4 season, Produces C

10%

1.5 wins

No Injury, Produces A

20%

10 wins

No Injury, Produces B

10%

6 wins

No Injury, Produces C

10%

3 wins

Explanation / Answer

Ok, we have this table

The probability of A: 30%

The probability of B: 40%

The probability of C: 30%

Outcome Probability Return/Production Gets Hurt, Misses Whole Season 10% 0 Gets Hurt, Misses 1/2 season, Produces B 20% 1.5 Gets Hurt, Misses 1/2 season, Produces C 10% 0.75 Gets Hurt, Misses 1/4 season, Produces B 10% 3 Gets Hurt, Misses 1/4 season, Produces C 10% 1.5 No Injury, Produces A 20% 10 No Injury, Produces B 10% 6 No Injury, Produces C 10% 3