Mathematics For Practical Applications Worksheet - 2011 Page 7
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16Exam #3
1.)
In 1897, all three outfielders for the Phillies batted at least .400. Billy Hamilton hit
.404 and Sam Thompson and Ed Delahanty each hit .407. We will view their
batting averages as probabilities, assume that all at bats are independent events
and ignore walks, etc.
a.)
Assume that the three bat right after each other in one inning. What is the
probability that all three get hits?
b.)
Assume that the three bat right after each other in one inning. What is the
probability that all three make outs?
c.)
If what is the probability that Hamilton gets a hit but Thompson and
Delahanty make outs?
d.)
If Delahanty has two at bats, what is the probability that he gets hits both
times?
e.)
If Hamilton bats six times, what is the probability he gets at least one hit?
f.)
If Delahanty and Hamilton bat, what is the probability that one, but not
both, gets a hit?
2.)
In 1969, Tommie Agee, Cleon Jones, Ron Swoboda, Art Shamsky, Rod Gaspar,
and Amos Otis were the main outfielders for the New York Mets. We are
interested in how many different groups of outfielders they could have had.
a.)
Is this a permutations problem or a combinations problem?
b.)
How many different groups were possible?
3.)
a.)
Draw a tree diagram to illustrate the flipping of three coins.
b.)
What is the probability of having exactly 2 heads?
c.)
What is the probability of having at least 2 heads?
4.)
You are making a license plate. It has 3 letters followed by 4 numbers. How
many different license plates can be made?
5.)
In their lunch menu, the Olive Garden restaurant in Fort Smith, offers nine
appetizers, three soups, two salads, thirty-four entrees, forty-two beverages and
eight desserts. If you order one appetizer, one soup, one salad, one entrée, one
beverage and one dessert, how many different meals could you order?
6.)
A box contains 8 arthropods, 7 cephalopods and 5 paramecia. You reach into
the box and pull out a creature at random. You then pull out another creature.
What is the probability that you pull out two cephalopods?
7.)
Fifteen people have formed a baseball team. We are interested in the number of
nine player batting orders that can be created from the fifteen players.
a.)
Is this a combination problem or a permutation problem?
b.)
How many different lineups are possible?
8.)
You put $5400 in the bank. The account gets an annual percentage rate of
interest of 3.21% compounded quarterly. The money is left in the account for 4
years. No other money is added or removed from the accounts.
a.)
Without inserting any numbers, write the formula you will need for this
problem.
b.)
Without doing any simplification, insert the right numbers in the right
places in the formula.
c.)
How much money will you have at the end of four years?
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