Question

The student council is hosting a drawing to raise money for scholarships. They are selling tickets for $5 each and will sell 800 tickets. There is one $1,000 grand prize, three $200 second prizes, and twelve $30 third prizes. You just bought a ticket. Find the expected value for your profit. Round to the nearest cent.

Answer 1

Let X is a random variable shows the profit. Here X can take values $5, -$1000+$5 =-$995 , -$200+$5 = -$195, -$30+$5 =-$25.

P(X = -995) = 1/800 =0.00125

P(X = -195) = 3/800 =0.00375

P(X=-25) = 12 / 800 = 0.015

P(X =+5) = (800 -(1+3+12)) /800 = 0.98

Following table shows the calculations for expected values:

X	P(X=x)	xP(X=x)
5	0.98	4.9
-25	0.015	-0.375
-195	0.00375	-0.73125
-995	0.00125	-1.24375
Total	1	2.55

So

The expected value for your profit is $2.55.