Name: _____________________________
Period: ________ Date: _______________
Numbers 1-3: Calculate the mean.
1.)
x
0
1
2
3
4
5
P(x)
0.528
0.360
0.098
0.013
0.001
0.000
Advanced Modeling
Expected Value
2.)
x
0
1
2
3
4
5
3.)
P(x)
0.02
0.15
0.29
0.26
0.16
0.12
x
0
1
2
3
4
5
6
P(x)
0.539
0.351
0.095
0.014
0.001
0.000
0.000
4.) In the Illinois Pick 3 lottery game, you pay $0.50 to select a sequence of three digits, such as 342. If you
select the same sequence of three digits that are drawn, you win and receive $350.
a.) How many different selections are possible?
b.) What is your probability of winning?
c.) If you win, what is your net profit?
d.) Calculate the expected value (I want to see a chart!).
e.) If you play the Illinois Pick 4 lottery game, the expected value is -$0.25. Which game is the better bet, the
Pick 3 or the Pick 4? Explain.
5.) In New Jersey’s Pick 4 lottery game, you pay $0.50 to select a sequence of four digits such as 4231. If you
select the same sequence of digits that are drawn, you win and receive $2788.
a.) How many different selections are possible?
b.) What is your probability of winning?
c.) If you win, what is your net profit?
d.) Calculate the expected value (I want to see a chart!).
e.) If you play the Illinois Pick 4 lottery game, the expected value is -$0.25. Which game is the better bet, the
New Jersey Pick 4 or the Illinois Pick 4? Explain.
6.) There is a 0.9986 probability that a randomly selected 30-year-old male lives through the year (based on
data from the U.S. Department of Health and Human Services). A Fidelity life insurance company charges
$161 for insuring that the male will live through the year. If the male does not survive the year, the policy
pays out $100,000 as a death benefit.
a.) From the perspective of the 30-year-old male, what are the values corresponding to the two events of
surviving the year and not surviving?
b.) If the 30-year-old male purchases the policy, what is his expected value? (I want to see a chart!)
c.) Can the insurance company expect to make a profit from many such policies? Explain.
7.) There is a 0.9968 probability that a randomly selected 50-year-old female lives through the year (based on
data from the U.S. Department of Health and Human Services). A Fidelity life insurance company charges
$226 for insuring that the female will live through the year. If the female does not survive the year, the policy
pays out $50,000 as a death benefit.
a.) From the perspective of the 50-year-old female, what are the values corresponding to the two events of
surviving the year and not surviving?
b.) If the 50-year-old female purchases the policy, what is her expected value? (I want to see a chart!)
c.) Can the insurance company expect to make a profit from many such policies? Explain.