Question

A local club plans to invest $10000 to host a baseball game. They expect to sell tickets worth $29924. 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 29924

Answer 1

Interpretations:
- If 29924 is the final amount received when the game is held, the expected final amount from investing is
E = 0.2(0) + 0.8(29924) = 0.8·29924 = 23,939.20.

- If you want expected profit relative to keeping the $10,000 in the bank (i.e. net gain/loss), compute net outcomes:
Rain: −10,000; No rain: 29,924 − 10,000 = 19,924.
Expected profit = 0.2(−10,000) + 0.8(19,924) = −2,000 + 15,939.20 = 13,939.20.

So the expected final amount is $23,939.20, which is an expected gain of $13,939.20 over leaving the $10,000 in the bank.