Math 101.01
Exam 2
11 February, 1999
Name: ________________________
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All pertinent work must be shown clearly, neatly, and legibly!
Points will be deducted for missing, incorrect or unclear work.
No partial credit will be given to an incorrect result without work shown.
Draw a circle or a box around your answer. Answers do not need to be completely simplified.
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1.
(10 points) BI-Mart carries 56 different types of St. Valentine's candy. How many ways can the folks
at BI-Mart arrange 4 different types of candy in a display at the front of the store if the order of the
candy in the display matters?
2.
6 (SIX!) cards are dealt from a standard 52-card deck.
a. (10 points) What is the probability of being dealt exactly 3 Sevens?
b.
(5 points) What are the odds of being dealt exactly 3 Sevens?
c.
(12 points) What is the probability of being dealt a 3-of-a-kind and a pair? (If you're not sure what
a 3-of-a-kind or a pair is, ask.)
3.
(10 points) If Delbert owns 13 hats, a pair of pants, 2 belts, 2 shirts, and 16 pocket protectors. How
many different "outfits" can Delbert wear? (Each "outfit" is a hat, a pair of pants, a belt, a shirt, and a
pocket protector.)
4.
Roulette is a game involving a bowl-like wheel sitting in the center of a table. The wheel has numbers
from 1 to 36, plus 0 and 00 placed around the edge. The dealer spins the wheel and drops a metal ball
into the bowl. As the wheel slows, the ball comes to rest on one of the 38 numbers. Wagers are made
on which number or what type of number the ball will stop on. For example, a person may wager $10
on "odd." If the ball stops on an odd number the better wins $10. If the number is not odd, then the
$10 wager is lost.
a. (12 points) What is the expected value of wagering $10 on "odd"?
b.
(5 points) How much money should a person expect to win or lose if they bet $10 on "odd" 50
times?
5.
Imagine that there is a bowl of those St. Valentine's Day miniature candy hearts on the desk in front of
you. The bowl contains 53 hearts in all; 22 of the hearts say "I Dig U", 16 of the hearts say "Fax Me",
and the rest say "Buzz Off."
a. (12 points) If you pick one heart out of the jar that says "Fax Me" and eat it, what is the
probability that the next heart you pick out of the jar will also say "Fax Me"?
b.
6.
(12 points) Now imagine that instead of picking one heart out of the bowl as you did in part (a),
you picked 4 hearts out of the bowl. What is the probability that all 4 will say "Buzz Off"?
(12 points) In the game of keno, what if the probability of selecting 6 numbers on your playing card
and having exactly four of the numbers be winning numbers? Recall that in Keno, one chooses
numbers from 1 - 80. Exactly 20 of those numbers are "winners" and 60 of them are "losers."