Homework 2
The following homework set has two types of problems. Those labeled “SS” are selfstudy
problems that do not need to be turned in. However, there are problems that I suggest you complete
to ensure that you understand all the material in the class. The problems not labeled SS should be
submitted for a grade. In general, the SS problems are easier than the graded problems, so they
can be used to practice and build expertise before doing the graded problems.
•
Oncampus students:
Submit nonSS problems by class time on Wednesday, September
21st. No electronic submissions will be accepted.
•
Offcampus students:
Submit nonSS problems via Sakai by Wednesday, September 28th.
Combinatorics
Use combinatorics to solve the following problems:
SS1. Find the number of possible combinations for a combination lock that has a combination
consisting of three numbers from the set 1–60. Find the number of combinations under these
three scenarios:
(a) The lock is a traditional “combination lock” consisting of a rotating dial that can be
pointed to any of 60 different numbers in a specific order. Depending on the mechanical
implementation of the lock, repeats may or may not be allowed. Let’s assume that we
can have repeats.
(Answer: 216,000)
(b) Now assume we have the same type of lock, but the implementation is such that repeats
are
not
allowed.
(Answer: 205,320)
(c) Now suppose we have a different type of combination lock. For instance, one with 60
push buttons, where the lock opens if you push in the three correct buttons. Now order
doesn’t matter and repeats are not allowed.
(Answer: 34220)
SS2.
(a) How many ways can 3 boys and 3 girls sit in a row?
(Answer: 720)
(b) How many ways can 3 boys and 3 girls sit in a row if the boys and the girls are each to
sit together?
(Answer: 72)
(c) In how many ways if only the boys must sit together?
(Answer: 144)
(d) In how many ways if no two people of the same sex are to sit together?
(Answer: 72)
1. Calculate the probabilities of winning the first four prizes (the Grand Prize through the
$100 prize) of the Powerball lottery (see
http://www.powerball.com/powerball/pb
prizes.asp
) and verify if the posted probabilities (under the erroneous title “Odds”) are
correct.
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SS3. Two cards are randomly drawn from an ordinary playing deck. What is the probability that
they form a blackjack? That is, what is the probability that one of the cards is an ace and the
other one is either a ten, a jack, a queen, or a king?
(Answer: 128/2652)
SS4. Poker dice is played by simultaneously rolling five dice. show that
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 Spring '11
 Wang
 Conditional Probability, Probability, Probability theory, Probability space, monty hall problem

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