Suppose you play a game where you pay $100 dollars to participate and have a 50% chance of winning nothing, a 10% chance of winning $1,100, a 20% chance of winning $600 and a 25% chance of losing $650.What is the expected value of participating in the game?
A)$100
B)$0
C)-$100
D)$1,050

Question

Quizplus · Accepted Answer

The expected value (EV) is calculated by multiplying each outcome by its probability and summing these products. EV = (0.5 * $0) + (0.1 * $1,100) + (0.2 * $600) - (0.25 * $650) = $0 + $110 + $120 - $162.50 = $67.50. Since you pay $100 to participate, the net expected value is $67.50 - $100 = -$32.50. However, none of the options correctly reflects this calculation. Based on the provided options, the closest correct approach to calculating expected value would still result in none of the options being correct. The explanation provided is based on the standard method for calculating expected value, but it appears there was a mistake in my calculation. Correcting my approach: EV = (0.5 * $0) + (0.1 * $1,100) + (0.2 * $600) + (0.25 * -$650) = $0 + $110 + $120 - $162.50 = $67.50. However, considering the initial payment of $100 to participate should actually be subtracted from the winnings, not added as a separate step. The correct calculation should factor in the cost as part of the outcomes. Given the misunderstanding in the explanation, the correct expected value calculation should directly consider the outcomes relative to the cost of playing, which was not accurately reflected in the initial response.

Suppose You Play a Game Where You Pay $100 Dollars