Find the expected value.
-Suppose you pay $1.00 to roll a fair die with the understanding that you will get back $3.00 for rolling a 1 or a 2, nothing otherwise. What is your expected value of your gain or loss?
A)$0.00
B)-$1.00
C)$3.00
D)$1.00

Question

Quizplus · Accepted Answer

The expected value is calculated by multiplying each outcome by its probability and then summing those values. Rolling a 1 or a 2 (2 outcomes out of 6) gives you $3.00, so the expected gain from those rolls is 2/6 * $3.00 = $1.00. For the other 4 outcomes, you gain nothing but lose your $1.00 bet, so the expected loss is 4/6 * -$1.00 = -$0.67. Adding these together, $1.00 - $0.67 = $0.33, but since you initially paid $1.00 to play, your net expected value is $0.33 - $1.00 = -$0.67. However, this calculation seems to have an error in considering the initial payment as part of the expected value calculation. Correctly, the expected gain should account for the initial bet as part of the outcomes. The correct calculation is: Expected value = (1/3 * $3.00) + (2/3 * $0) - $1.00 = $1.00 - $1.00 = $0.00.

Find the Expected Value