Question

It is on the Discrete probability distribution.
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) Verify that this is a probability distribution.

Amount Wins	$200	$100	$50	$0	Total
Probability	1/200 = 0.005	2/200 = 0.01	3/200 = 0.015	(200-6)/200 = 194/200 = 0.97	1

As all the probability > 0 and total is one

Hence this is a probability distribution

(b) Recognizing that John spent $10 to buy a ticket, determine the expected value of this raffle to him.

Expected value = (200*0.005 ) + ( 100*0.01 ) + (50*0.015 ) + 0*0.97 - 10 ( tickets bought of $10 )

Expected value = 1 + 1 + 0.75 + 0 - 10

Expected value = -$7.25

He will loose $7.25