A local club plans to invest $10000 to host a baseball game. They expect to sell tickets worth $23567. 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?

Question

Rain No Rain
Probability 0.2
Leave money in bank 10000 10000

Invest in Baseball game 0 23567

Answer 1

To calculate the expected value of investing in the baseball game, we need to consider both scenarios: the event of rain and the event of no rain, along with their respective probabilities and outcomes.

1. Outcomes:

   • If it rains (with a probability of 0.2), the club will sell no tickets and will lose the entire investment of $10,000.
   • If it does not rain (with a probability of 0.8), the club will sell tickets worth $23,567 and will keep that amount.

2. Expected Values for Each Scenario:

   • Rain:

     • Probability = 0.2
     • Outcome = -$10,000 (since they lose their investment)
     • Expected Value = \(0.2 \times (-10,000) = -2,000\)

   • No Rain:

     • Probability = 0.8
     • Outcome = $23,567
     • Expected Value = \(0.8 \times 23,567 = 18,853.60\)

3. Total Expected Value:

   • Now, we combine the expected values from both scenarios: \[ \text{Total Expected Value} = \text{Expected Value (Rain)} + \text{Expected Value (No Rain)} \] \[ \text{Total Expected Value} = -2,000 + 18,853.60 = 16,853.60 \]

Thus, the expected value of investing in the baseball game is $16,853.60.