Volunteers working to raise funds for a new community library sold 1000 raffle tickets at $10 each. Tickets are to be randomly drawn and prizes are awarded as follows: one prize of $1,000, twenty prizes of $50 and one hundred prizes of $20. What is the expected value of this raffle to you if you buy just one ticket? What is the expected value of this raffle if you buy all of the tickets?
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How do you solve 4* 0.32 using place value and renaming?
How can you solve 4*0.32 using place value and renaming.
To calculate the expected value of the raffle, we need to determine the probability of winning each prize amount and then multiply it by the corresponding prize value.
For the first question, where you buy just one ticket:
1. Probability of winning the $1,000 prize: There is only one prize, so the probability is 1/1000.
2. Probability of winning a $50 prize: There are twenty prizes, so the probability is 20/1000.
3. Probability of winning a $20 prize: There are one hundred prizes, so the probability is 100/1000.
Now, let's calculate the expected value:
Expected value = (Probability of winning $1,000 prize × $1,000) + (Probability of winning a $50 prize × $50) + (Probability of winning a $20 prize × $20)
Expected value = (1/1000 × $1,000) + (20/1000 × $50) + (100/1000 × $20)
Simplifying:
Expected value = $1 + $1 + $2
Expected value = $4
Therefore, when you buy just one ticket, the expected value of the raffle is $4.
For the second question, where you buy all the tickets:
To find the expected value if you buy all of the tickets, we need to consider the probabilities after each ticket is drawn.
1. Probability of winning the $1,000 prize:
After each ticket is drawn, the probability of winning the $1,000 prize changes. Since you bought all the tickets, the probability after the first ticket is drawn would be 1/999, after the second ticket 1/998, and so on. We need to calculate the sum of all these probabilities.
2. Probability of winning a $50 prize:
Similar to the previous case, after each ticket is drawn, the probability of winning a $50 prize changes. The sum of these probabilities needs to be calculated as well.
3. Probability of winning a $20 prize:
Again, after each ticket is drawn, the probability of winning a $20 prize changes. The sum of these probabilities needs to be calculated.
Then, we can calculate the expected value using the same formula as before:
Expected value = (Probability of winning $1,000 prize × $1,000) + (Probability of winning a $50 prize × $50) + (Probability of winning a $20 prize × $20)
Keep in mind that calculating the probabilities after each ticket is drawn can be more time-consuming, given the large number of tickets. However, conceptually, this is how the expected value would be determined if you buy all of the tickets.