Question

John bought one of 200 raffle tickets for $10. The sponsors then randomly select one grand prize worth $200, two second prizes worth $100 each, and three third prizes at $50 each. (a) Verify that this is a probability distribution. (b) Recognizing that John spent $10 to buy a ticket, determine the expected value of this raffle to him.

Answer 1

a.

prize (in dollars)	P(prize)
200	1/200
100	2/200
50	3/200
0	(200-1-2-3)/200 = 194/200

it is probability distibution because all probabilities are in range [0,1]

and sum of probabilities is 1

b.

E(vale) = sum of value*P

= sum of (prize-cost)*P(prize)

= (200-10)*1/200 + (100-10)*2/200 + (50-10)*3/200 + (0-10)*194/200

= -7.25 dollars

(please upvote)