Final answer:
The expected value of the game is approximately -$5.24, meaning a player would expect to lose an average of $5.24 per game if they play repeatedly.
Step-by-step explanation:
The subject of this question is Mathematics, specifically related to probability and expected value calculations often encountered at the high school level. The student is tasked with finding the expected value of a game where they have a 1/42 chance of winning 67 units (dollars/points) and a 41/42 chance of losing 7 units. To calculate the expected value (EV), we use the formula:
EV = (Probability of Winning) × (Amount Won) + (Probability of Losing) × (Amount Lost)
Plugging in the values from the question, we have:
EV = (1/42) × 67 + (41/42) × (-7)
From this, we can compute:
EV = 67/42 + (-287/42)
EV = (67 - 287) / 42
EV = -220 / 42
EV = -5.23809524, which rounds to approximately -5.24 when considering two decimal places.
If you play this game repeatedly, over a long string of games, you would expect to lose $5.24 per game, on average. Therefore, playing this game is not a good strategy if intending to win money, as the expected value indicates an average loss.
The complete question is: In a game, you have a probability of winning 67 with 1/42 and a probability of losing 7 with 41/42. What is your expected value? is: