lottery offers one $900 prize, two $700 prize, two $400 prize and five $200 prize. One thousand tickets are sold at $5. Find the expectation if a person buys two tickets

To find the expectation, we need to first calculate the probability of winning each prize and then multiply it by the value of the prize. Here's how to do it step-by-step:

Step 1: Calculate the total number of prizes for each category:
- $900 prize: 1 prize
- $700 prize: 2 prizes
- $400 prize: 2 prizes
- $200 prize: 5 prizes

Step 2: Calculate the total number of tickets sold:
- 1000 tickets

Step 3: Calculate the probability of winning each prize:
- For the $900 prize: 1/1000 (since there is only 1 prize out of 1000 tickets)
- For the $700 prize: 2/1000 (since there are 2 prizes out of 1000 tickets)
- For the $400 prize: 2/1000 (since there are 2 prizes out of 1000 tickets)
- For the $200 prize: 5/1000 (since there are 5 prizes out of 1000 tickets)

Step 4: Calculate the expected value of each prize:
- For the $900 prize: (1/1000) * $900 = $0.90
- For the $700 prize: (2/1000) * $700 = $1.40
- For the $400 prize: (2/1000) * $400 = $0.80
- For the $200 prize: (5/1000) * $200 = $1.00

Step 5: Calculate the total expected value:
- Add up the expected values of each prize: $0.90 + $1.40 + $0.80 + $1.00 = $4.10

Step 6: Multiply the total expected value by the number of tickets bought:
- since a person buys two tickets, multiply $4.10 by 2:
$4.10 * 2 = $8.20

Therefore, the expectation if a person buys two tickets is $8.20.

To calculate the expectation if a person buys two tickets for the lottery, we need to find the probability of winning each prize and its corresponding value.

There are a total of 1,000 tickets sold, and a person buys two of them. Therefore, the probability of winning a particular prize can be determined by dividing the number of tickets for that prize by the total number of tickets sold.

Let's calculate the probability and expected value for each prize:

1. $900 prize:
Number of tickets: 1
Probability of winning: 1/1,000 = 0.001
Expected value: $900 * 0.001 = $0.9

2. $700 prize:
Number of tickets: 2
Probability of winning: 2/1,000 = 0.002
Expected value: $700 * 0.002 = $1.4

3. $400 prize:
Number of tickets: 2
Probability of winning: 2/1,000 = 0.002
Expected value: $400 * 0.002 = $0.8

4. $200 prize:
Number of tickets: 5
Probability of winning: 5/1,000 = 0.005
Expected value: $200 * 0.005 = $1

Now, we can calculate the overall expectation by summing up the expected values for each prize:

$0.9 + $1.4 + $0.8 + $1 = $4.1

Therefore, the expectation if a person buys two tickets is $4.1.

each ticket has an expectation of

(900+2*700+2*400+5*200)/1000 = $4.10