Question

(1 point) Prizes and the chances of winning in a sweepstakes are given in the table below. Prize $10,000,000 $150,000 $50,000 $10,000 $800 Chances 1 chance in 200,000,000 1 chance in 100,000,000 1 chance in 90,000,000 1 chance in 1,000,000 1 chance in 200,000 A watch valued at $601 chance in 8,000 (a) Find the expected value (in dollars) of the amount won by one entry. (b) Find the expected value (in dollars) if the cost of entering this sweepstakes is the cost of a postage stamp (34 cents)

Answer 1

Expected number of amount won by one entry will be

p(r)

Let us first find the probability p(x)

Prize(X)	Chances	P(X=x)
$10,000,000	1 Chance in 200,000,000	P(X=$10000000)=1/200,000,000
$150,000	1 Chance in 100,000,000	P(X=$150,000)=1/100,000,000
$50,000	1 Chance in 90,000,000	P(X=$50,000)=1/90,000,000
$10,000	1 Chance in 1,000,000	P(X=$10000)=1/1000,000
$800	1 Chance in 200,000	P(X=$800)=1/200,000
A watch valued at $ 60	1 Chance in 8000	P(X=$60)=1/8000

+150,000× 100,000. 000 800 × 200,000 E(r) = Σ r) = 10. 000. 000× 200.000.000 ( 200,000, 0 -1-ct60 × 8000 50.000 × 10,000 1000.000 90,000, 000

E(z) = 〉 ·rp(x) = 0.05+0.00 15+0.000556+0.01+0.004+0.0075= 0.073

Expected value of amount won by one entry is 0.073

b)

The expected value if the cost of entering this sweepstakes is the cost of a postage stamp 34 cents will be

Expected value=0.073−0.34=−0.267