Question

I buy one of 250 raffle tickets for $10. The sponsors then randomly select 1 grand prize worth $300, 2 second prizes worth $120 each, and 3 third prizes worth $50 each. Below is the discrete probability distribution for this raffle.

Prize	P(x)
Grand	1/250
Second	2/250
Third	3/250
None	244/250

(a) Recognizing that I spent $10 to buy a ticket, determine the expected value of this raffle to me as a player. Round your answer to the nearest penny.


(b) What is an accurate interpretation of this value?

It represents how much you would win every time you play the game.

It is meaningless because you can't actually win or lose this amount.     

It represents how much you would lose every time you play the game.

It represents the per-game average you would win/lose if you were to play this game many many times.

(c) Based on your answers, would this raffle be a good financial investment for you and why? There is only one correct answer and reason.

Yes, because the expected value is positive.

Yes, because the expected value is negative.     

No, because the expected value is positive.

No, because the expected value is negative.

Answer 1

following information has been generated using ms-excel

Prize	amount(x)	P(x)	P(x)	x*P(x)
Grand	300	1/250	0.004	1.2
Second	120	2/250	0.008	0.96
Third	50	3/350	0.012	0.6
None	0	244/250	0.976	0
		sum=	1	2.76

(a) expected value of X i,.e. E(X)=sum(x*P(x))=2.76

since ticket cost is $10, so net gain/loss=2.76-10=7.24

(b)  It represents the per-game average you would win/lose if you were to play this game many many times.

(c) No, because the expected value is negative.

( net gain gain is negative)