Find the expected value of the random variable. Round to the nearest cent unless stated otherwise.
-Suppose you pay $2.00 to roll a fair die with the understanding that you will get back $4.00 for rolling a 4 or a 5, nothing otherwise. What is your expected value?
A)-$2.00
B)$2.00
C)-$0.67
D)$4.00

Question

Find the expected value of the random variable. Round to the nearest cent unless stated otherwise.
-Suppose you pay $2.00 to roll a fair die with the understanding that you will get back $4.00 for rolling a 4 or a 5, nothing otherwise. What is your expected value? 
A)-$2.00
B)$2.00
C)-$0.67
D)$4.00

Quizplus · Accepted Answer

The expected value is calculated by multiplying each outcome by its probability and summing these products. Here, the probability of rolling a 4 or a 5 is 2/6 (since there are two favorable outcomes out of six possible outcomes), and the payout for these outcomes is $4.00. For any other roll, the outcome is -$2.00 (the cost to play). Thus, the expected value is (2/6)*$4.00 + (4/6)*(-$2.00) = $8/6 - $8/6 = -$0.67.

Find the Expected Value of the Random Variable