Question

A raffle offers one $8000.00 prize, one $4000.00 prize, and five $1600.00 prizes. There are 5000 tickets sold at $5 each. Find the expectation if a person buys one ticket.

Answer 1

The expectation is
`E(1 )= -\$ 1`

Explanation:

From the question we are told that

The first offer is
`x_1 = \$ 8000`

The second offer is
`x_2 = \$ 4000`

The third offer is
`\$ 1600`

The number of tickets is
`n = 5000`

The price of each ticket is
`p= \$ 5`

Generally expectation is mathematically represented as

`E(x)=\sum x * P(X = x )`

`P(X = x_1 ) = (1)/(5000)` given that they just offer one

`P(X = x_1 ) = 0.0002`

Now

`P(X = x_2 ) = (1)/(5000)` given that they just offer one

`P(X = x_2 ) = 0.0002`

Now

`P(X = x_3 ) = (5)/(5000)` given that they offer five

`P(X = x_3 ) = 0.001`

Hence the expectation is evaluated as

`E(x)=8000 * 0.0002 + 4000 * 0.0002 + 1600 * 0.001`

`E(x)=\$ 4`

Now given that the price for a ticket is
`\$ 5`

The actual expectation when price of ticket has been removed is

`E(1 )= 4- 5`

`E(1 )= -\$ 1`