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

Answer:

The expectation is  $E(1 )= -\ 1$

Step-by-step 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

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

     $P(X = x_1 ) = \frac{1}{5000}$    given that they just offer one

    $P(X = x_1 ) = 0.0002$    

 Now  

     $P(X = x_2 ) = \frac{1}{5000}$    given that they just offer one

     $P(X = x_2 ) = 0.0002$    

 Now  

      $P(X = x_3 ) = \frac{5}{5000}$    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

      $E(1 )= 4- 5$

      $E(1 )= -\ 1$