How Do I Fill Out This PDF Table for This Problem?

Question

I need help with this problem for my statistics class.

Question: "A theater group holds a fund-raiser. It sells 100 raffle tickets for $7 apiece. Suppose you purchase four tickets. The prize is two passes to a Broadway show, worth a total of $150"

1. So I understand we are interested in the amount of winnings and the random variable X is the amount of winnings. The list of values that X may take on is -28, 122. I just need help constructing the PDF below (my answer has to be rounded to two decimal places).

X P(X= x) x · P(X = x)

Loss
Profit

I also need help answering the question below:

1. If this fund-raiser is repeated often and you always purchase four tickets, what would be your expected average winnings per raffle? (answer must be rounded to two decimal places.)

Thanks for your help

Answer 1

Mikaela

Well if one of your four tickets comes up, your win is 122 (you get tickets worth 150 but you have paid 28. 150-28 = 122)

if your tickets don't come up, you lose 28 (you pay 28 for the tickets getting nothing).

What is chance of you winning. Well 4/100. as 4 tickets out of 100 win.

So

x p(X=x) x. p (X=x)

-28 0.96 -26.88

122 0.04 4.88

So expected outcome = -26.88 + 4.88 = -22, so if you played N times where N is a large number you would expect to lose 22N $.