Question

If you play the carnival game that costs $20 and there are two outcomes - winning a prize worth $100 or losing the $20, what is the expected value (average value) of playing the game?

a) $20
b) $40
c) $60
d) $80

Answer 1

Cannot accurately answer the question regarding the expected value of playing the carnival game without probability values of winning and losing; the provided options cannot be correctly determined.

Step-by-step explanation:

To calculate the expected value of playing the carnival game, we need to take into account the probability of winning and losing as well as the associated values of those outcomes. Here, the probability of each outcome is not given, so we cannot calculate the exact expected value without making assumptions. However, with the details provided, we can consider each outcome, where 'W' represents winning with a prize worth $100, 'L' represents losing $20, and 'P(W)' and 'P(L)' are their respective probabilities:

• E(W) = P(W) × $100
• E(L) = P(L) × - $20

The total expected value (EV) would then be E(W) + E(L). To determine the best answer, additional information regarding the actual probabilities of winning and losing is required. Without this information, the expected value cannot be calculated and hence no answer from the provided options can be selected with confidence.

If the probabilities of winning and losing were known, we could use the formula for expected value (EV):

EV = (Probability of Winning × Value of Winning Prize) + (Probability of Losing × Value of Losing)