find the expected value of the prize
value $0 $1 $5 $20
probability 0.9359 0.05 0.01 0.003
To find the expected value of the prize, you need to multiply each value by its corresponding probability, and then add up the results.
Let's calculate it step by step:
1. Multiply each value by its probability:
- For the value $0, the probability is 0.9359, so the contribution to the expected value is 0 * 0.9359 = $0.
- For the value $1, the probability is 0.05, so the contribution to the expected value is 1 * 0.05 = $0.05.
- For the value $5, the probability is 0.01, so the contribution to the expected value is 5 * 0.01 = $0.05.
- For the value $20, the probability is 0.003, so the contribution to the expected value is 20 * 0.003 = $0.06.
2. Add up the contributions:
- $0 + $0.05 + $0.05 + $0.06 = $0.16.
Therefore, the expected value of the prize is $0.16.