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A local club plans to invest $10000 to host a baseball game. They expect to sell tickets worth $27675. But if it rains on the day of game, they won't sell any tickets and the club will lose all the money invested. If the weather forecast for the day of game is 20% possibility of rain,what is the expected value of investing in the baseball game?
Rain No Rain
Probability 0.2
Leave money in bank 10000 10000
Invest in Baseball game 0 27675
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Answered by
GPT-5 mini
AI
Interpret the outcomes as final amounts received after the event.
EV(final) = 0.2·0 + 0.8·27,675 = 0.8·27,675 = 22,140.
So the expected value of investing is $22,140. Relative to the $10,000 you started with, the expected profit is 22,140 − 10,000 = $12,140. (Keeping the money in the bank would give $10,000, so investing has a higher expected return.)
EV(final) = 0.2·0 + 0.8·27,675 = 0.8·27,675 = 22,140.
So the expected value of investing is $22,140. Relative to the $10,000 you started with, the expected profit is 22,140 − 10,000 = $12,140. (Keeping the money in the bank would give $10,000, so investing has a higher expected return.)
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