332 .UNCERTAINTY IN FUTURE EVENTS -
What would be his expected outcome if he invests the
$1000?'
10-12 The MSU football team has 10 games scheduled for
next season. The business manager wishes to estimate
how much money the team can be expected to have
left over after paying the season's expenses, including
any postseason "bowl game" expenses. From records
for the past season and estimates by informed people,
the business manager has assembled the following
data:Based on the business manager's data, what is the
expected net income for the team next season?
(Answer: $355,000)
10-13 In the New Jersey and Nevada gaming casinos, craps
is a popular gambling game. One of the many bets
available is the "Hard-way 8." A $1 bet in this fash-
ion will win the player $4 if in the game the pair of
dice come up 4 and 4 prior to one of the other ways of
totaling 8. For a $1 bet, what is the expected result?
(Answer:80jt)
10-14 If your interest rate is 8%, what is the expected value
of the present worth of the "extra" insurance payments
in Problem 1O-9? (Answer: $528.7)
10-15 A decision has been made to perform certain re-
pairs on the outlet works of a small dam. For a par-
ticular 36-inch gate valve, there are three available
alternatives:
(a)Leave the valve as it is.
(b)Repair the valve.
(c) Replace the valve.If the valve is left as it is, the probability of a
failure of the valve seats, over the life of the project,
is 60%; the probability of failure of the valve stem is
50%; and of failure of the valve body is 40%.
If the valve is repaired, the probability of a fail-
ure of the seats, over the life of the project, is 40%;
of failure of the stem is 30%; and of failure of the
body is 20%. If the valve is replaced, the probability
of a failure of the seats, over the life of the project, is
30%; of failure of the stem is 20%; and offailure of
the body is 10%.
The present worth of cost of future repairs and
service disruption of a failure of the seats is $10,000;
the present worth of cost of a failure of the stem.is
$20,000; the present worth of cost of a failure of the
body is $30,000. The cost of repairing the valve now
is $10,000; and of replacing it is $20,000. If the crite-
rion is to minimize expected costs, which 'alternative
is best?
10-16 A man went to Atlantic City with $500 and placed
100 bets of $5 each, one after another, on the same
number on the roulette wheel. There are 38 numbers
on the wheel and the gaming casino pays 35 times
the amount bet if the ball drops into the bettor's num-
bered slot in the roulette wheel. In addition, the bettor
receives back the original $5 bet. Estimate how much
money the man is expected to win or lose in Atlantic
City.
10-17 A factory building is located in an area subject to
occasional flooding by a nearby river. You have been
brought in as a consultant to determine whether flood-
proofing of the building is economically justified. The
alternatives are as follows:
(a)Do nothing. Damage in a moderate flood is
$10,000 and in a severe flood, $25,000.
(b)Alter the factory building at a cost of $15,000
to withstand moderate flooding without damage
and to withstand severe flooding with $10,000
damages.
(c) Alter the factory building at a cost of $20,000 to
withstand a severe flood without damage.
In any year the probability of flooding is as follows:
0.70, no flooding of the river; 0.20, moderate flood-
ing; and 0.10, severe flooding. If inter.est is 15%
and a 15-year analysis period is used, what do you
recommend?
10-18 An industrial park is being planned for a tract of land
near the river. To prevent flood damage to the in-
dustrial buildings that will be built on this low-lyingProb-
Situation ability Situation. Net Income
Regular season Regular season
Win 3 games 0.10 Win 5 or $250,000
Win 4 games 0.15 fewer
Win 5 games 0.20 games
Win 6 games 0.15 Win6to8 400,000
Win 7 games 0.15 games
Win 8 games 0.10
Win 9 games 0.07 Win 9 or 10 600,000
Win 10 games 0.03 gamesPostseason Postseason Additional
Bowl game 0.10 Bowl game income of
$100,000