MDM4UI
Unit 3 - Lesson 10
Chapter Review
Questions are taken from:
p. 357 – 359 # 1 – 17.
Questions from the “Chapter Test” (p. 360 – 361) will be discussed
next day.
p. 357 # 1.
A bag of marbles contains seven whites, five blacks, and eight cat’seyes. Determine the probability that a randomly drawn marble is
(a) a white marble
P(white marble)
n( white marbles)

n(all marbles in bag )
7

20
(b) a marble that is not black
P(not black marble)
n(not black marble)
15


n(all marbles in bag )
20
3

4
p. 357 # 2.
When a die was rolled 20 times, 4 came up five times.
(a) Determine the empirical probability of rolling a 4
with a die based on the 20 trials.
NOTE: The empirical probability of a particular event (also called experimental
relative frequency probability) is determined by dividing the number of
times that the event actually occurs in an experiment by the number of
trials.
n(4' s rolled )
5 1
P(rolling a 4) 


n(total rolls taken) 20 4
(b) Determine the theoretical probability of rolling a 4
with a die based on the 20 trials.
NOTE: The theoretical probability of a particular event is deduced from analysis
of the possible outcomes. It does not require an actual experiment.
Let A  {roll a 4 on a die}
n( A) 1
P( A) 

n( S ) 6
p. 357 # 3.
Estimate the subjective probability of each event and provide a
rationale for your decision.
(a) All classes next week will be cancelled.
Select a LOW percentage. It is very unlikely
that ALL would be cancelled unless the school
was damaged and required lengthy repair.
I will say..... P(A) = 1%
(b) At least one severe snow storm will occur in your area next
winter.
Select a HIGH percentage. It is very likely
that AT LEAST ONE severe storm will occur
in this "snow belt" region.
I will say..... P(A) = 90%
p. 357 # 4.
Determine the odds in favour of flipping three coins and
having them all turn up heads.
Let A  {flipping heads}
P( A)  n ( A)
n( S )
1
2
P( A  A  A) 
1 1 1
 
2 2 2
1

8
 the odds of flipping 3 coins all turned up HEADS is
1: 7
p. 357 # 5.
A restaurant owner conducts a study that measures the frequency of
customer visits in a given month. The results are recorded in the
following table.
(a) The odds that a customer visited
Number
Number of
of Visits
Customers
EXACTLY 3 times
1
4
2
6
3
7
4 or more
3
7
P(exactly 3 visits) 
20
 the odds would be 7:13.
(b) The odds that a customer visited FEWER than 3 times
P( fewer than 3 visits)  10  1
2
 the odds would be 1:1. 20
(c) The odds against a customer visited MORE than 3 times
3
P( fewer more than 3 visits) 
20
 the odds against would be 17:3.
p. 357 # 6.
Suppose three marbles are selected at random from the bag of
marbles in question 1.
(a) Draw a tree diagram to illustrate all possible outcomes.
W
W
B
CE
W
B
B
CE
W
CE
B
CE
W
B
CE
W
B
CE
W
B
CE
W
B
CE
W
B
CE
W
B
CE
W
B
CE
W
B
CE
W
B
CE
p. 357 # 6.
(b) Are all possible outcomes equally likely? Explain.
Since probabilities vary among branches, not all of the outcomes
are equally likely.
(c) Determine the probability that all three selected marbles are
cat’s-eyes.
Let A  {all 3 marbles are cat's-eyes}
n ( A)
P( A) 
n( S )
56
14
8 C3



1140
285
20 C3
p. 357 # 6.
(d) Determine the probability that none of the marbles drawn are
cat’s-eyes.
Let B  { NO marbles are cat's-eyes}
P ( B )  n ( A)
n( S )
12 C3

20 C3
220

1140
11

57
p. 357 # 7.
The Sluggers baseball team has a starting line-up consisting of
nine players, including Tyrone and his sister Amanda. If the
batting order is randomly assigned, what is the probability that
Tyrone will bat first, followed by Amanda?
Arrange the remaining 7 players
1  1 
7 P7
P
9 9
5040

362880
1

72
p. 357 # 8.
A three-member athletics council is to be randomly chosen from ten
students, five of whom are runners. The council positions are
president, secretary, and treasurer. Determine the probability that
(a) the committee is comprised of all runners.
P
60
1


P(all runners) 
720
12
10 P3
5 3
(b) the committee is comprised of the three eldest runners.
P
6
1


P(three eldest) 
720
120
10 P3
3 3
(b) the committee is comprised of the three eldest runners.
1
1

P(three eldest in specific role) 
720
10 P3
p. 358 # 9.
Classify each of the following pairs of events as INDEPENDENT or
DEPENDENT.
First Event
Second Event
Hitting a home run
Catching a pop fly
while at bat
while in the field
Staying up late
Sleeping in the next
day
Completing your
Passing your
calculus review
calculus exam
Randomly
selecting a shirt
Randomly
selecting a tie
INDEPENDENT
or
DEPENDENT?
INDEPENDENT
DEPENDENT
DEPENDENT
INDEPENDENT
p. 357 # 10.
Bruno has just had job interviews with two separate firms. Golden
Enterprises and Outer Orbit Manufacturing. He estimates that he has
a 40% chance of receiving a job offer from Golden and a 75% chance
of receiving an offer from Outer Orbit.
(a) What is the probability that Bruno will receive both job offers?
NOTE : These events are independent.
Let G  {will work for Golden}
Let O  {will work for Outer Orbit}
P(G) 
0.4
P(O) 
0.75
P(G  O)  P(G)  P(O)  0.4  0.75  0.3
 there is a 30% chance that Bruno receives both job offers.
(b) Is Bruno applying the concept of theoretical, empirical, or
subjective probability? Explain.
Since Bruno is making a personal estimate of the probabilities,
he is applying the concept of SUBJECTIVE probability.
p. 358 # 11.
Karen and Klaus are the parents of James and twin girls Britta and
Kate. Each family member has two shirts in the wash. If a shirt is
pulled from the dryer at random, what is the probability that the shirt
belongs to
(a) Klaus, if it is known that the shirt belongs to one of the parents?
2
1
n(Klaus)
P(Klaus) 


2
4
n(Parents)
(b) Britta, if it is known that the shirt is for a female?
2
1
n(Britta)
P(Britta) 


3
6
n(female)
p. 358 # 11. (continued)
(c) Kate, if it is known that the shirt belongs to one of the twins?
P(Kate) 
n(Kate)

n(Twin)
2
1

2
4
(d) Karen or James.
P(Karen  James)  n(Karen or James in same stage)
n(all shirts)
22
4


10
10
p. 358 # 12.
During a marketing blitz, a telemarketer conducts phone solicitations
continuously from 16 00 to 20 00. Suppose that you have a 20%
probability of being called during the blitz. If you generally eat dinner
between 18 00 and 18 30, how likely is it that the telemarketer will
interrupt your dinner?
P(receiving a call)  0.20
P(eating when phone rings) 
n(time spent eating)
n(total hours of blitz)
0.5

 0.125
4.0
P(receiving a call  eating)  P(receiving call)  P(eating when phone rings)
 0.20
 0.025

0.125
 there is a 2.5% chance that the telemarketers will interrupt your supper.
p. 358 # 13.
Classify each pair of events as mutually exclusive or non-mutually
exclusive.
First Event
Second Event
Randomly selecting
Randomly selecting
a classical CD
a rock CD
Birthday occurs
on a Wednesday
Birthday occurs
on a weekend
hamburger
hamburger
with cheese
with no onions
rolling a perfect
square with a die
rolling an even
number with a die
Mutually Excl.
or
Non-Mutually Excl.
mutually excl.
mutually excl.
non-mutually excl.
non-mutually excl.
p. 357 # 14.
(a)
Determine the probability of drawing either a 5 or a black face
card from a standard deck of cards.
P(5 or black face)  P(5)  P(black face)
4
6
=

52
52
10

52
5

26
p. 357 # 15.
In the data management class of 26 students, there are 9 with blonde
hair, 7 with glasses, and 4 with blonde hair and glasses.
(a)
Draw a Venn diagram to illustrate this
situation.
S
14
5
Blonde Hair
(b)
4
3
Wear Glasses
If a student is selected at random, what is the probability that
the student will have either blonde hair or glasses?
P(blonde  glasses)  P(blonde)  P(glasses)  P(blonde  glasses)

9
26


12
26

7
26
6
13

4
26
p. 357 # 16.
Of 150 students at a school dance, 110 like pop songs and 70 like
heavy-metal songs. A third of the students like both pop and heavymetal songs.
(a)
If a pop song is played, what are the odds in favour of a
randomly selected student liking the song?
110  Odds
110 : 40
in favour is
150
What are the odds in favour of a student disliking both pop and
heavy-metal songs?
NOTE: A Venn diagram helps here.
P(pop song liked) 
(b)
P(P'  HM') 
 Odds:
20
150
S
20
Pop
60
50
20
20 :130
Heav y -Metal
To Be Continued…
Homework
p. 357 – 359 # 6 - 17.