MDM4UIUnit 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 whitemarble

p. 357 # 1.

A bag of marbles contains seven whites, five blacks, and eight cat’s-eyes. Determine the probability that a randomly drawn marble is

7

20

( )

( )

n white marbles

n all marbles in bag

(a) a white marble

(b) a marble that is not black

( )P not black marble( )

( )

n not black marble

n all marbles in bag 15

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.

(b) Determine the theoretical 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.

(4 ' ) 5 1( 4)

( ) 20 4

n s rolledP rolling a

n total rolls taken

NOTE: The theoretical probability of a particular event is deduced from analysis of the possible outcomes. It does not require an actual experiment.Let {roll a 4 on a die}

( ) 1( )

( ) 6

A

n AP A

n S

p. 357 # 3.

Estimate the subjective probability of each event and provide a

rationale for your decision.

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%

(a) All classes next week will be cancelled.

(b) At least one severe snow storm will occur in your area next winter.

90

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) = %

p. 357 # 4.

Determine the odds in favour of flipping three coins and having them all turn up heads.

Let {flipping heads}

( )

A

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.

Number of Visits

Number of

Customers

1 4

2 6

3 7

4 or more 3

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.

( 3 )P exactly visits

(a) The odds that a customer visited

EXACTLY 3 times7

20

the odds would be 7:13.(b) The odds that a customer visited FEWER than 3 times

( 3 )P fewer than visits 10

20

the odds would be 1:1.

1

2

(c) The odds against a customer visited MORE than 3 times

( 3 )P fewer more than visits3

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

B

CE

W

B

CE

W

BCEW

BCEW

BCE

W

B

CE

W

B

CE

W

BCEW

BCEW

BCE

W

BCEW

BCEW

BCE

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 {all 3 marbles are cat's-eyes}

( )

A

P A

( )

( )

n A

n S

8 3

20 3

C

C

56

1140

14

285

p. 357 # 6.

(d) Determine the probability that none of the marbles drawn are

cat’s-eyes.

Let { NO marbles are cat's-eyes}

( )

B

P B

( )

( )

n A

n S12 3

20 3

C

C

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?

7 7P

9 9P

Arrange the remaining 7 players

1 1

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.

(b) the committee is comprised of the three eldest runners.

5 3

10 3

(all runners)P

PP

60

720

1

12

3 3

10 3

(three eldest)P

PP

6

720

1

120

(b) the committee is comprised of the three eldest runners.

10 3

1(three eldest in specific role)P

P

1

720

p. 358 # 9.

Classify each of the following pairs of events as INDEPENDENT or

DEPENDENT.

First Event Second EventINDEPENDENT

or

DEPENDENT?

Hitting a home run

while at bat

Catching a pop fly

while in the fieldINDEPENDENT

Staying up lateSleeping in the next

dayDEPENDENT

Completing your

calculus review

Passing your

calculus examDEPENDENT

Randomly

selecting a shirt

Randomly

selecting a tieINDEPENDENT

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.

Let {will work for Golden}G

(a) What is the probability that Bruno will receive both job offers?: These events are independent.NOTE

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 0.3there 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.

(a) Klaus, if it is known that the shirt belongs to one of the parents?

(Klaus)P

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

(Klaus)

(Parents)

n

n

2

4

1

2(b) Britta, if it is known that the shirt is for a female?

(Britta)P (Britta)

(female)

n

n

2

6

1

3

p. 358 # 11. (continued)

(c) Kate, if it is known that the shirt belongs to one of the twins?

(Kate)P (Kate)

(Twin)

n

n

2

4

1

2

(d) Karen or James.

(Karen James)P (Karen or James in same stage)

(all shirts)

n

n2 2

10

4

10

p. 358 # 12.

(receiving a call)P

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?

0.20

(eating when phone rings)P (time spent eating)

(total hours of blitz)

n

n

0.5

4.0 0.125

(receiving a call eating) (receiving call) P(eating when phone rings)P P

0.20 0.125 0.025

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 Mutually Excl.

or

Non-Mutually Excl.

Randomly selecting

a classical CD

Randomly selecting

a rock CD mutually excl.

Birthday occurs

on a WednesdayBirthday occurs

on a weekendmutually excl.

hamburger

with cheese

hamburger

with no onionsnon-mutually excl.

rolling a perfect

square with a die

rolling an even

number with a dienon-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.

(5 or black face)P (5) (black face)P P4 6

=52 52

10

525

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

Wear GlassesBlonde Hair

4 35

14

(b) If a student is selected at random, what is the probability that the student will have either blonde hair or glasses?

(blonde glasses)P (blonde) (glasses) (blonde glasses)P P P 9 7 4

26 26 26

12

26

6

13

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 heavy-

metal songs.

(a) If a pop song is played, what are the odds in favour of a randomly selected student liking the song?

(pop song liked)P in favourOdds is 110 : 40110

150(b) What are the odds in favour of a student disliking both pop and

heavy-metal songs?

(P' HM')P 20

150

Odds: 20 :130

NOTE: A Venn diagram helps here. S

Heavy-Metal

Pop

50 2060

20

To Be Continued…

Homework p. 357 – 359 # 6 - 17.