Question

Solve the problem. 9) Suppose that you roll a pair of honest dice. If you roll a total of 6 , you win $ 18 \); if you roll a total of 11 , you win $ 72 \); if you roll any other total, you los

Answer 1

expected value = -$0.75

Explanation:

Suppose that you roll a pair of honest dice. If you roll a total of 6 , you win $18; if you roll a total of 11 , you win $72; if you roll any other total, you lose $9. What is the expected value of 1 roll of the dice.

There are 36 possible outcomes.

The 5 outcomes with a sum of 6 are (5,1), (4,2), (3,3), (2,4), (1,5).

The 2 outcomes with a sum of 11 are (6,5), (5, 6).

The other 29 outcomes lose $9.

expected value = 29/36 × (-$9) + 5/36 × ($18) + 2/36 × ($72)

expected value = -$7.25 + $2.5 + $4

expected value = -$0.75