Question

A community youth group is having a raffle to raise funds. Several community businesses have donated prizes. The prizes and their retail values are listed in the table below. Each prize will be given away, regardless of the number of raffle tickets sold. Tickets are sold for $16 each. Determine the expected value of a ticket, and discuss whether it would be to your financial advantage to buy a ticket under the given circumstances. (Enter your answers to two decimal places.)

Prize	Retail Value	Number of These Prizes to Be Given Away
new car	$21,530	1
a cell phone and a one- year subscription	$930	1
a one-year subscription to an Internet service provider	$600	2
dinner for two at a local restaurant	$110	2
a one-year subscription to the local newspaper	$180	20

(a) 1000 tickets are sold.
$   

Should you buy a ticket?

Yes No     

(b) 2000 tickets are sold.
$  

Should you buy a ticket?

YesNo     

(c) 3000 tickets are sold.
$  

Should you buy a ticket?

YesNo    

Answer 1

a)

X	P(X)	X*P(X)
21530	1/1000 = 0.001	21.530
930	0.001	0.9300
600	0.002	1.2000
110	0.002	0.2200
180	0.02	3.6000
0	0.974	0.0000

mean = E[X] = Σx*P(X) =            27.48

expected value = 27.48-16 = 11.48

yes, you should buy a ticket

b)

X	P(X)	X*P(X)
21530	1/2000 = 0.0005	10.765
930	0.0005	0.4650
600	0.001	0.6000
110	0.001	0.1100
180	0.01	1.8000
0	0.987	0.0000

mean = E[X] = Σx*P(X) =            13.74

expected value=13.74-16= -2.26

there is loss on average

so, you should not buy a ticket

c)

X	P(X)	X*P(X)
21530	0.00033333	7.177
930	0.00033333	0.3100
600	0.00066667	0.4000
110	0.00066667	0.0733
180	0.00666667	1.2000
0	0.99133333	0.0000

mean = E[X] = Σx*P(X) =            9.1600

expected value per ticket = 9.16 - 16 = -6.84

so, you should not buy a ticket