Question

Find the the expected value. Thank you.

Problem 2: A player chooses one of the numbers 1 through 4. After the choice has been made, two regular four-sided (tetrahedral) dice are rolled, with the sides of the dice numbered 1 through 4 If the number chosen appears on the bottom of exactly one die after it has been rolled, then the player wins $1 dollar. If the number chosen appears on the bottom of both of the dice, then the player wins $2 dollars. If the number chosen does not appear on the bottom of either of the dice, the player loses $1 dollar. What is the expected return to the player, in dollars, for one roll of the dice?

Answer 1

Probability of a number on a 4-sided die = 1/4 =0.25

Probability of not the selected number= 1-0.25 =0.75

Probability of number on bottom of exactly one die out of 2 die, P(one)= 0.25*0.75 +0.75*0.25 = 0.375

Expected win at exactly one number at bottom of 2 die= $1

Probability of the number on bottom of both die, P(both) = 0.25*0.25 = 0.0625

Expected win at both number at bottom of 2 die= $2

Probability of the number on bottom of none of the die, P(none) = 0.75*0.75 = 0.5625

Expected lose at number not on the bottom of 2 die= -$1

Expected return =

= 0.375*1 + 0.0625*2 + 0.5625*(-1)

=  - $0.0625

Expected return is -$0.0625.