Respuesta :
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:
[tex]E(X)=\sum x.P(X)[/tex]
Compute the probability distribution of X as follows:
Prize Amount (X) P (X) x · P (X)
1 Grand prize $3000 [tex]\frac{1}{1250}=0.0008[/tex] [tex]\$3000\times 0.0008=2.4[/tex]
1 Second prize $450 [tex]\frac{1}{1249}=0.0008[/tex] [tex]\$450\times 0.0008=0.36[/tex]
10 Third prize $25 [tex]\frac{10}{1248}=0.008[/tex] [tex]\$25\times 0.008=0.2[/tex]
No prize -$4 [tex]1-\sum P(Win)\\=0.9904[/tex] [tex]-\$4\times 0.9904=-3.9616[/tex]
TOTAL 1.0000 -1.0016
Thus, the expected value of the winnings for a single-ticket purchase is -$1.0016.
