Question

A raffle offers a first prize of $1000, 2 second prizes of $300, and 20 third prizes of $10 each. If 20000 tickets are sold at 25 cents each, find the expected winnings for a person buying 1 ticket What are the expected winnings? cents (Round your answer to the nearest whole cent)

Answer 1

The expected winnings for a person buying 1 ticket is -0.2.

Explanation:

Given : A raffle offers a first prize of $1000, 2 second prizes of $300, and 20 third prizes of $10 each. If 20000 tickets are sold at 25 cents each, find the expected winnings for a person buying 1 ticket.

To find : What are the expected winnings?

Solution :

There are one first prize, 2 second prize and 20 third prizes.

Probability of getting first prize is
`(1)/(20000)`

Probability of getting second prize is
`(2)/(20000)`

Probability of getting third prize is
`(20)/(20000)`

A raffle offers a first prize of $1000, 2 second prizes of $300, and 20 third prizes of $10 each.

So, The value of prizes is

`(1)/(20000)* 1000+(2)/(20000)* 300+(20)/(20000)* 10`

If 20000 tickets are sold at 25 cents each i.e. $0.25.

Remaining tickets = 20000-1-2-20=19977

Probability of getting remaining tickets is
`(19977)/(20000)`

The expected value is

`E=(1)/(20000)* 1000+(2)/(20000)* 300+(20)/(20000)* 10-(19977)/(20000)* 0.25`

`E=(1000+600+200-4994.25)/(20000)`

`E=(-3194.25)/(20000)`

`E=-0.159`

Therefore, The expected winnings for a person buying 1 ticket is -0.2.