You Buy a lottery ticket to a lottery that cost $10 per ticket. There only 100 tickets available to be sold in the lottery. In this lottery there are one $500 prizes, two $100 prizes and four $25 prices. Find your expected gain or loss. Do you still want to play the raffle?
To find your expected gain or loss, you need to calculate the expected value of the lottery ticket. The expected value is the average amount you can expect to win or lose on each ticket.
In this case, we need to consider the probabilities of winning each prize and the value of each prize. Let's calculate it step by step:
1. Calculate the probability of winning each prize:
- There is 1 ticket that wins the $500 prize, so the probability of winning the $500 prize is 1/100.
- There are 2 tickets that win the $100 prize, so the probability of winning the $100 prize is 2/100.
- There are 4 tickets that win the $25 prize, so the probability of winning the $25 prize is 4/100.
2. Calculate the value of each prize:
- The $500 prize is worth $500.
- The $100 prize is worth $100.
- The $25 prize is worth $25.
3. Calculate the expected value:
- To calculate the expected value, multiply the probability by the value for each prize and sum them up:
Expected value = (1/100 * $500) + (2/100 * $100) + (4/100 * $25)
After calculating, the expected value is $5.
Based on the expected value, you can expect to gain $5 on average per ticket you purchase. Since the ticket costs $10, the expected loss is $5.
Therefore, your expected gain or loss from playing the lottery is a loss of $5.
Considering this information, it is up to you whether you still want to play the raffle.