UMBC CMSC203 Discrete Structures, Section 06, Spring 2016
Homework 11, Due Thursday, 04/28
For each of these questions, you must show your work and explain
your answer.
You will have to write down some English sentences.
Answers that consist of a single number will receive
less than 50% credit!
When factorials are involved, leave your answer in terms of factorials
(e.g., 5!/(3! ⋅ 2)).
 Marble Placement.
In a board game, you have 19 indistinguishable marbles that you can
place in 5 distinguishable locations. You must place at least 2
marbles at each location, but are otherwise allowed to place as
many or as few marbles at each location. How many different ways
can you make these placements?
 Balls & Bins.
You have 13 balls that you throw at 5 bins labeled A, B,
C, D and E. Our assumption is that when a ball is thrown at the
bins, there is an equal probability that the ball lands in any
particular bin. Also, the ball will always land in one of the
bins. Each bin is large enough to hold any number of balls.

You throw the 13 balls, one at a time, at the bins. What is the
probability that exactly 3 balls land in bin A? Justify your
answer.

You throw the 13 balls, one at a time, at the bins. What is the
probability that 4 or fewer balls land in bin B? Justify your
answer.
 Two Urns. [Adapted from Epp, 3/e.]
You have two urns. One urn holds 5 red balls and
13 yellow balls. The second urn holds 9 red balls and
11 yellow balls. You pick one ball using this procedure:
randomly pick one of the two urns with equal probability, then
pick a ball from the chosen urn so that each ball is chosen
with equal probability.
 What is the probability that the chosen ball
is red?
 If the chosen ball is red, what is the
probability that the chosen ball came from the first urn?
 Odd Man Out.
Four friends play a game called Odd Man Out. They each flip a fair
coin. If 1 person has heads and the other 3 have tails, then the
person with heads is the odd man. Similarly, if 1 person has tails
and the other 3 have heads, then the person with tails is the odd
man. What is the probability of having an odd man after each person
flips just once? Explain your answer.
 Plastic Utensils.
You randomly pick utensils from a box with plastic knives, forks
and spoons. Each time you pick, there is an equal probability of
picking any of the utensils remaining in the box. Initially, the box
holds 4 forks, 3 spoons and 7 knives.
Note: Show all of your work and explain your answers.
 Suppose you pick 3 utensils without replacement.
What is the probability that you picked a fork, a spoon and
a knife (in any order)?
 Suppose that you pick 2 utensils without replacement.
What is the probability that the second utensil you picked is a knife?
 Suppose that you pick 2 utensils without replacement.
What is the conditional probability that the second utensil
you picked is a knife given that the first utensil is a fork?
 Suppose that you pick 2 utensils without replacement.
What is the probability that at least one of the two is a spoon?
Last Modified:
22 Apr 2016 10:22:21 EDT
by
Richard Chang
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