A theater group holds a fund-raiser. It sells 100 raffle tickets for $8 apiece.

Question

A theater group holds a fund-raiser. It sells 100 raffle tickets for $8 apiece. Suppose you purchase four tickets. The prize is two passes to a Broadway show, worth a total of $150.

Part (a)

What are you interested in here?

the total number of raffle tickets sold
the price of the raffle tickets    
the amount of winnings
the type of fund-raiser

Part (b)

In words, define the Random Variable X.

the amount of money made selling raffle tickets
the total number of raffle tickets sold    
the amount of winnings
the number of passes to the Broadway show

Part (c)

List the values that X may take on.

8, 1180,
1, 2, ..., 100    
1, 2, 3, 4
32, 118

Part (d)

Construct a PDF. (Round your answers to two decimal places.)

            X.        P(X = x)       x · P(X = x)

Loss
Profit

Part (e)

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

Explanation / Answer

a)

the amount of winnings

b)

the amount of winnings

c)

-32, 118(150-32)

d)

X.        P(X = x)       x · P(X = x)

Loss -32 4C2/100C2 =
Profit 118

e)

If this fund-raiser is repeated often and you always purchase four tickets, what would be your expected average winnings per raffle? (Round your answer to two decimal places.)
$ -31.82

X P(X) XP(X) Loss -32 0.998788 -31.9612 Profit 118 0.001212 0.14303 -31.8182

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