Question

Your school’s baseball team sells 1250 raffle tickets at $4 each. The grand prize is a $3000 boat. The second prize is a $450 grill. There are also ten $25 gift certificates. Calculate the expected value of the winnings for a single-ticket purchase. Show the work that leads to your answer.

Answer 1

Answer:

The expected value of the winnings for a single-ticket purchase is -$1.0016.

Step-by-step explanation:

The total number of tickets sold is, N = 1250.

Cost of one ticket is, $4.

Let X = amount of prize.

The prize distribution is as follows:

1 Grand price = $3000

1 Second prize = $450

10 Third prize = $25

The expected value X can be computed using the formula:

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

Compute the probability distribution of X as follows:

     Prize        Amount (X)         P (X)                    x · P (X)

1 Grand prize    $3000         $\frac{1}{1250}=0.0008$     $\ 3000\times 0.0008=2.4$

1 Second prize  $450          $\frac{1}{1249}=0.0008$      $\ 450\times 0.0008=0.36$

10 Third prize      $25          $\frac{10}{1248}=0.008$        $\ 25\times 0.008=0.2$

No prize             -$4      $1-\sum P(Win)\\=0.9904$   $-\ 4\times 0.9904=-3.9616$

TOTAL                              1.0000                            -1.0016

Thus, the expected value of the winnings for a single-ticket purchase is -$1.0016.