A lottery offers one $900 prize, one $600 prize, three $400 prizes, and five $100 prizes. One thousand tickets are sold at $6 each. Find the expectation of a person buys five tickets.

Total amount of prizes

= 900+600+3*400+5*100
= $3200
Total number of tickets
= 1000
expected value of prizes for each ticket sold =3200/1000=$3.2
What is the expected value of 5 tickets?

To find the expectation, we need to calculate the expected value for each prize and then sum them up.

First, let's find the probabilities of winning each prize category:

- The probability of winning the $900 prize is 1/1000, as there is only one $900 prize out of 1000 tickets.
- The probability of winning the $600 prize is also 1/1000, as there is only one $600 prize out of 1000 tickets.
- The probability of winning a $400 prize is 3/1000, as there are three $400 prizes out of 1000 tickets.
- The probability of winning a $100 prize is 5/1000, as there are five $100 prizes out of 1000 tickets.

Next, let's calculate the expected value for each prize category:

- Expected value of winning the $900 prize = (1/1000) * $900 = $0.9
- Expected value of winning the $600 prize = (1/1000) * $600 = $0.6
- Expected value of winning a $400 prize = (3/1000) * $400 = $1.2
- Expected value of winning a $100 prize = (5/1000) * $100 = $0.5

Now, let's find the total expected value by summing up the expected values for each prize category:

Total expected value = ($0.9 + $0.6 + $1.2 + $0.5) * 5 = $6.2 * 5 = $31

Therefore, the expectation of a person who buys five tickets is $31.

To find the expectation of a person who buys five tickets in the lottery, we need to calculate the expected value. The expected value is determined by multiplying the value of each outcome by its corresponding probability and summing them up.

Let's start by calculating the total amount of money collected from selling tickets. Since one ticket costs $6 and a person buys five tickets, the total amount collected is $6 multiplied by 5, which gives $30.

Now, let's calculate the probability of winning each prize:

- The probability of winning the $900 prize is 1 / 1000, as there is only one winning ticket out of 1000 sold.
- The probability of winning the $600 prize is also 1 / 1000, as there is only one winning ticket for this prize too.
- The probability of winning one of the three $400 prizes is 3 / 1000 since there are three winning tickets.
- The probability of winning one of the five $100 prizes is 5 / 1000 since there are five winning tickets.

Next, we multiply the value of each prize by its corresponding probability:

Expected value = (Value of $900 prize) × (Probability of winning $900 prize)
+ (Value of $600 prize) × (Probability of winning $600 prize)
+ (Value of $400 prize) × (Probability of winning $400 prize)
+ (Value of $100 prize) × (Probability of winning $100 prize)

Expected value = ($900) × (1 / 1000) + ($600) × (1 / 1000) + ($400) × (3 / 1000) + ($100) × (5 / 1000)

Calculating these values:

Expected value = $0.9 + $0.6 + $1.2 + $0.5 = $3.2

Therefore, the expectation for a person who buys five tickets in the lottery is $3.2. This means that, on average, they can expect to win $3.2 per five tickets bought.

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