Deck 7: Probability: Living With the Odds

Question 1

Provide an appropriate response.
An insurance company sells an insurance policy for $1000. If there is no claim on a policy, the company makes a profit of $1000. If there is a claim on a policy, the company faces a large loss on
That policy. The expected value to the company, per policy, is $250.
Which of the following statements is (are)true?

A)B and C
B)A and C
C)B only
D)C only

Answer 1

A

Question 2

Provide an appropriate response.
Which of the following statements makes sense?

A)B and C
B)C only
C)A only
D)All of them
E)A and C

Answer 2

C

Question 3

Provide an appropriate response.
Chantal noted that there are two equally likely outcomes when you flip a fair coin and heads is one of those outcomes. She concluded that the probability of getting heads on a flip of a fair coin is 1/2 .
Which method did Chantal use?

A)Empirical method
B)Relative frequency method
C)Subjective method
D)Theoretical method

Answer 3

D

Question 4

Provide an appropriate response.
A card is selected at random from a standard deck of 52 cards. Let Which of the following is (are)true?

Question 5

Provide an appropriate response.
The permutation formula can be used to determine which of the following?

Question 6

Provide an appropriate response.
When using the counting rules to count the number of possible outcomes, the combinations formula can be used in which of the following situations?

A)When repetitions are not allowed and the order of arrangement is important
B)When repetitions are allowed and the order of arrangement is unimportant
C)When repetitions are not allowed and the order of arrangement is unimportant
D)When repetitions are allowed and the order of arrangement is important

Question 7

Provide an appropriate response.
Which of the following are examples of independent events?

A)Two people in the same family falling ill in the same week
B)Two laughs by different people watching the same movie in a theater
C)Two consecutive wins by a football team
D)Two archeological discoveries at different locations, at the same time

Question 8

Provide an appropriate response.
Event A is that it rains in Santa Cruz tomorrow. Event B is that rains in Paris, France tomorrow. Are events A and B:

A)D
B)B
C)A
D)C

Question 9

Provide an appropriate response.
A game involves tossing a fair coin 200 times. For each tail that appears you lose $1. For each head that appears, you win $1.
After 100 tosses, there have been 40 heads and 60 tails. At this point, with 100 tosses to go, what
Can you conclude?
A: You are more likely to lose than to win.
B: You are still equally likely to win or lose because in the long run there should be 50% heads.
C: In the next 100 tosses you are likely to get more heads than tails.

A)B and C
B)A and C
C)A only
D)B only

Question 10

Provide an appropriate response.
The combination formula can be used to determine which of the following?

A)A only
B)C only
C)B and C
D)B only
E)A and B

Question 11

Provide an appropriate response.
Suppose that S and T are mutually exclusive events. Which of the following statements is true?

A)S and T must also be independent.
B)S and T may or may not be independent.
C)S and T cannot possibly be independent.

Question 12

Provide an appropriate response.
Suppose that 4 items are to be selected from N items and that repetitions are not allowed. Which of the following is true?

A)There are 4 times as many permutations as combinations.
B)There are 4 times as many combinations as permutations.
C)There are 24 times as many combinations as permutations.
D)There are 24 times as many permutations as combinations.

Question 13

Provide an appropriate response.
Event A is that Lisa votes for Candidate A in the gubernatorial election and event B is that she votes for candidate B. Are events A and B:

A)B
B)D
C)A
D)C

Question 14

Provide an appropriate response.
When using the counting rules to count the number of possible outcomes, the permutation formula can be used in which of the following situations?

A)When repetitions are allowed and the order of arrangement is important
B)When repetitions are allowed and the order of arrangement is unimportant
C)When repetitions are not allowed and the order of arrangement is important
D)When repetitions are not allowed and the order of arrangement is unimportant

Question 15

Provide an appropriate response.
When a balanced die is rolled, the probability that a four will appear is Which of the following statements is a reasonable conclusion?

A)C only
B)A and B
C)B and C
D)B only
E)All of them

Question 16

Provide an appropriate response.
Which of the following events has a probability of 1? A: I will get a perfect score on my math test if I study
B: I will die some day
C: The world will go on turning if I fail my test

A)A and B
B)All of them
C)B only
D)B and C
E)A and C

Question 17

Provide an appropriate response.
When a balanced die is rolled, the probability that a six will appear is . Suppose that you have just rolled the die five times without getting a six. What is the probability that you will get a six on
The next roll of the die?

A)1
B)Greater than but less than 1
C)
D)0

Question 18

Provide an appropriate response.
When tossing a fair coin, which of the following events is more unlikely?

A)C
B)B
C)A
D)All are equally likely

Question 19

Provide an appropriate response.
In a large casino, the house wins on its blackjack games with a probability of 50.7%. Which of the following events is the most unlikely?
A: You win at a single game.
B: You come out ahead after playing forty times.
C: You win at a single game given that you have just won ten games in a row.
D: You win at a single game given that you have just lost ten games in a row.

A)D
B)B
C)A
D)C

Question 20

Provide an appropriate response.
Melissa estimates that the probability that she will marry her boyfriend is 0.6. Which method for determining probabilities did she use?

A)Theoretical method
B)Relative frequency method
C)Subjective method
D)Empirical method

Question 21

Write the word or phrase that best completes each statement or answers the question.
If you flip a fair coin 10 times would you be surprised if the coin comes up the same way
every time? What would be the probability of this?
If 2000 people all flip a fair coin 10 times, on average how many people could be expected
to get the same thing all 10 times?

Question 22

Write the word or phrase that best completes each statement or answers the question.
For a particular game at a casino, the expected winning for the player is -$0.87. How
would you interpret this statement?

Question 23

Write the word or phrase that best completes each statement or answers the question.
Explain what is wrong with the statement below.
It's amazing that someone won the $100,000 prize in the lottery tonight. The probability of
winning $100,000 is only 0.000000512.

Question 24

A fair coin is tossed 5 times. Which of the following statements is (are)true?

Question 25

Write the word or phrase that best completes each statement or answers the question.
A game is said to be "fair" if the expected value for winnings is 0, that is, in the long run,
the player can expect to win 0. Consider the following game. The game costs $1 to play and
the payoffs are $5 for red, $3 for blue, $2 for yellow, and nothing for white. The following
probabilities apply. What are your expected winnings? Does the game favor the player or
the owner?

Question 26

Write the word or phrase that best completes each statement or answers the question.
When two balanced dice are rolled, there are 36 possible outcomes. What is the probability that the sum of the numbers on the dice is 6 or 10?

Question 27

Write the word or phrase that best completes each statement or answers the question.
Suppose that the probability of winning at a single game of blackjack is 0.49. If you play
ten times in a row, what is the probability you will win all 10 times? Would you be
surprised? If 1000 people each play blackjack ten times in one evening, what is the
probability that at least one person wins all ten times? Would you be surprised?

Question 28

The permutation formula can be used to determine which of the following?

Question 29

A knight may win a tournament. He may also fail to win the love of his lady. Are these events overlapping? Why or why not?

A)Yes, because some ladies love winners
B)No, because not all ladies love all winners
C)Yes, because not all ladies love all winners
D)No, because all ladies love all winners

Question 30

A)B
B)A
C)D
D)C

Question 31

Sean flipped a coin 100 times and got heads 42 times. He concludes that the probability of getting heads on a flip of his coin is 0.42. Which method did Sean use?

A)Theoretical method
B)Empirical method
C)Multiplication method
D)Subjective method

Question 32

Find the expected value.
You are given 16 to 1 odds against tossing 4 tails in 4 tosses of a fair coin. This means that you win $16 if you succeed and you lose $1 if you fail. Find the expected value (to you)of the game. Round
To the nearest cent.

A)$0.06
B)-$0.06
C)$0.13
D)$1.00

Question 33

Question 34

Write the word or phrase that best completes each statement or answers the question.
Explain what is wrong with the statement below.
It's quite a coincidence - the chance that I would have the birthday I do have is only 1/365.

Question 35

Solve the problem. Round your answer to 2 decimal places when necessary.
A U.S. city with a population of 1.7 million reports 35,738 births. What is the birth rate in births per 1000 people?

A)2.1 births per 1000 people
B)47.57 births per 1000 people
C)21.02 births per 1000 people
D)210 births per 1000 people

Question 36

Question 37

Write the word or phrase that best completes each statement or answers the question.
Suppose a mathematician computed the expected winnings (to the player)of each of seven
different games in a casino. What would you expect to be true for all expected winnings?

Question 38

For the students at one college the expected value for "number of siblings" is 1. Which of the following statements is a reasonable conclusion?

A)If 100 students are selected at random, the average number of siblings for the 100 students will be close to 1.
B)If a student selected at random has 2 siblings, the next student selected will have no siblings.
C)If 4 students are selected at random, the average number of siblings for the 4 students will be 1.
D)If a student is selected at random, the most likely number of siblings for the student is 1.

Question 39

Write the word or phrase that best completes each statement or answers the question.
A card is selected randomly from a standard deck of 52 cards. Let Give examples of events B, C, and D such that A and B are independent, A and C are
dependent and overlapping, and A and D are non-overlapping.

Question 40

Which pair(s)of events is (are)independent? A and $B$ given the following: $P(A)=0.4, P(B)=0.3, P(A$ and $B)=0.16$ $C$ and $D$ given the following: $P(C)=0.4, P(D)=0.3, P(C \mid D)=0.4$

A) Neither pair
B) $C$ and $D$
C) $A$ and $B$
D) Both pairs

Question 41

Find the indicated probability. Round your answer to 6 decimal places when necessary.
A bag contains 7 red marbles, 4 blue marbles, and 1 green marble. What is the probability of choosing a marble that is not blue?

Question 42

Solve the problem.
Find the odds against drawing a heart when a card is drawn at random from a normal deck of 52 playing cards.

A)1 to 4
B)1 to 3
C)3 to 1
D)4 to 1

Question 43

Solve the problem.
Find the odds for getting two tails and a head when three fair coins are flipped.

A)1 to 7
B)5 to 3
C)3 to 8
D)3 to 5

Question 44

Find the indicated probability.
A die is rolled 100 times with the following results. Compute the empirical probability that the die comes up 2 or 3.

Question 45

Solve the problem. Round your answer to 5 decimal places when necessary.
The table shows the leading causes of death for one country in a single recent year. Assume a population of 86.5 million. How much greater is the risk of death by heart disease than the risk of death by stroke?

A)4.13793
B)3.72414
C)41.37931
D)0.00182

Question 46

Find the indicated probability. Round your answer to 6 decimal places when necessary.
What is the probability of not rolling a number larger than 4 with a fair die?

Question 47

Solve the problem.
How many different 4-letter sequences can be made using the first 11 letters of the alphabet? Assume that repetition of letters is allowed.

A)24
B)330
C)7920
D)14,641

Question 48

Solve the problem.
Find the odds for getting two heads when two fair coins are flipped.

A)4 to 1
B)1 to 4
C)1 to 3
D)3 to 1

Question 49

Find the indicated probability. Round your answer to 6 decimal places when necessary.
What is the probability that 4 randomly selected people all have different birthdays?

A)0.9891
B)0.9918
C)0.9729
D)0.9836

Question 50

Find the indicated probability. Round your answer to 6 decimal places when necessary.
The probability that a particular region in Mexico will be hit by a hurricane in any given year is 0.07. Find the probability that the region will be hit by a hurricane in 3 consecutive years.

A)0
B)0.0049
C)0.000343
D)0.21

Question 51

Evaluate the factorial expression.

Question 52

Solve the problem. Round your answer to 5 decimal places when necessary.

-The table shows the leading causes of death for one country in a single recent year. $\begin{array}{l|r}{\text { Cause of Death }} & \text { Deaths } \\\hline \text { Heart Disease } & 152,250 \\\text { Cancer } & 116,000 \\\text { AIDS } & 71,775 \\\text { Stroke } & 42,050 \\\text { Pulmonary Disease } & 40,745 \\\text { Accidents } & 30,450 \\\text { Diabetes } & 17,545 \\\text { Pneumonia } & 16,240 \\\text { Kidney Disease } & 8555\end{array}$ Assume a population of 72.5 million. What is the empirical probability of death by stroke during a single year?

A)0.0058
B)0.058
C)0.00058
D)0.000058

Question 53

Use the at least once rule to find the indicated probability.
Find the probability of at least one club when you draw cards from a standard deck 17 times; assume that you replace the card each time you draw , so there are always 52 cards to draw from.

A)0.003
B)0.744
C)0.992
D)0.008

Question 54

Solve the problem. Round your answer to 2 decimal places when necessary.
A country with a population of 103 million has 19,261 traffic fatalities. Find the fatality rate in deaths per 100,000 population.

A)1926 deaths per 100,000 people
B)187 deaths per 100,000 people
C)1.87 deaths per 100,000 people
D)18.7 deaths per 100,000 people

Question 55

Solve the problem.
Find the odds for drawing an ace when a card is drawn at random from a normal deck of 52 playing cards.

A)12 to 1
B)13 to 1
C)1 to 12
D)1 to 13

Question 56

Find the expected value.
Experience shows that a ski lodge will be full (199 guests)if there is a heavy snow fall in December, while only partially full (57 guests)with a light snow fall. What is the expected number of guests if
The probability for a heavy snow fall is .40? Assume that heavy snowfall and light snowfall are the
Only two possibilities.

A)119.4
B)142.2
C)79.6
D)113.8

Question 57

Solve the problem. Round your answer to 2 decimal places when necessary.
A certain U.S. city had 54 traffic fatalities last year. There were 3.3 million miles driven in the city.. Determine the traffic fatality rate per 1,000,000 miles driven.

A)16,363,636.36 fatalities per 1,000,000 miles driven
B)0.06 fatalities per 1,000,000 miles driven
C)1.64 fatalities per 1,000,000 miles driven
D)16.36 fatalities per 1,000,000 miles driven

Question 58

Solve the problem.
There are 7 finalists in a singing competition. If a person guesses randomly the top three winners (in any order), what is the probability that they
Will guess correctly?

Question 59

Solve the problem.
There are 5 members on a board of directors. If they must elect a chairperson, a secretary, and a treasurer, how many different slates of candidates are possible?

A)125
B)10
C)120
D)60

Question 60

Find the expected value.
In a large casino, the house wins on one of its games with a probability of 51,000%. All bets are 1 : 1 . If you win, you gain the amount you bet; if you lose, you lose the amount you bet.
If patrons bet a total of $900,000 on this game in one evening, how much should the casino expect
To earn?

A)$917,100,000
B)$459,000,000
C)$1.10052e+09
D)$458,550,000

Question 61

Find the indicated probability. Round your answer to 6 decimal places when necessary.
An IRS auditor randomly selects 3 tax returns from 50 returns of which 5 contain errors. What is the probability that she selects none of those containing errors?

A)0.0005
B)0.724
C)0.729
D)0.001

Question 62

Use the at least once rule to find the indicated probability.
Find the probability of at least one queen when you draw cards from a standard deck 11 times; assume you replace the card each time you draw , so there are always 52 cards to draw from.

A)0.035
B)0.415
C)0.585
D)0.958

Question 63

Find the expected value.
An insurance company will insure a $220,000 home for its total value for an annual premium of $590. If the company spends $30 per year to service such a policy, the probability of total loss for
Such a home in a given year is 0.001 and you assume either total loss or no loss will occur, what is
The company's expected annual gain (or profit)on each such policy?

A)-$220
B)$290
C)$340
D)$370

Question 64

Solve the problem.
A local department store sells carpets in 4 sizes. Each carpet comes in 3 different qualities. One of the sizes comes in 5 colors. The other sizes come in 2 colors. How many choices of carpet are there?

A)39
B)40
C)33
D)38

Question 65

Find the indicated probability. Round your answer to 6 decimal places when necessary.
If you are dealt two cards successively (with replacement of the first)from a standard 52-card deck, find the probability of getting a heart on the first card and a diamond on the second.

Question 66

Use the at least once rule to find the indicated probability.
A study conducted at a certain college shows that 64% of the school's graduates find a job in their chosen field within a year after graduation. Find the probability that among 5 randomly selected
Graduates, at least one finds a job in his or her chosen field within a year of graduating.

A)0.893
B)0.200
C)0.640
D)0.994

Question 67

Find the indicated probability. Round your answer to 6 decimal places when necessary.
Based on meteorological records, the probability that it will snow in a certain town on January 1st is 0.441. Find the probability that in a given year it will not snow on January 1st in that town.

A)2.268
B)0.789
C)0.559
D)1.441

Question 68

Find the indicated probability. Round your answer to 6 decimal places when necessary.
Two fair 6-sided dice are rolled. What is the probability that the sum of the two numbers on the dice is greater than 10?

Question 69

Find the indicated probability.
The following table show the results of a clinical trial for an allergy drug. What is the probability that a randomly selected person was given a placebo or improved? Round your answer to the nearest thousandth when necessary.

A)0.942
B)0.17
C)0.69
D)0.772

Question 70

Decide whether events A and B are overlapping or non-overlapping.
A card is drawn at random from a deck of cards. Event A is that the card selected is a queen and event B is that the card selected is a two.

A)Non-overlapping
B)Overlapping

Question 71

Find the indicated probability.
The following table displays the number of siblings for students at one middle school. Find the probability that a randomly selected student in the school has 2 siblings. Round your answer to the
Nearest thousandth.

A)0.263
B)0.200
C)0.125
D)0.188

Question 72

Find the indicated probability. Round your answer to 6 decimal places when necessary.
You are dealt two cards successively (without replacement)from a shuffled deck of 52 playing cards. Find the probability that the first card is a king and the second card is a queen.

Question 73

Evaluate the factorial expression.

Question 74

Solve the problem.
The table shows the prizes and probabilities of winning (on a single $1 ticket)for a particular state lottery. How much would you expect to win or lose if you bought one $1 ticket every day for a year?
Round to the nearest dollar.

Question 75

Use the relative frequency method to estimate the probability. Round your answer to 2 decimal places when necessary.
Every week, Joe plays chess with his father. Of the last 50 games, Joe has won 60% of the games. What is the probability that Joe will win the next game?

A)0.060
B)0.60
C)0.5
D)1

Question 76

Solve the problem.
A shoe store carries one brand of shoe in 5 different styles, 5 sizes, and 3 colors. How many different shoes are available of this one brand?

A)125
B)75
C)13
D)30

Question 77

Solve the problem. Round your answer to 2 decimal places when necessary.
In a recent year, there were 62 accidents in commercial aviation among major airlines over 15.5 million flight hours. Find the accident rate in units of accidents per 100,000 flight hours.

A)0.62 accidents per 100,000 flight hours
B)0.40 accidents per 100,000 flight hours
C)4 accidents per 100,000 flight hours
D)6.2 accidents per 100,000 flight hours

Question 78

Use the at least once rule to find the indicated probability.
The probability of winning $20 in a particular lottery is 0.04. What is the probability that you will get at least one $20 winner if you buy 90 tickets?

A)0.975
B)0.001
C)0.025
D)0.960

Question 79

Evaluate the factorial expression.

Question 80

Find the indicated probability. Round your answer to 6 decimal places when necessary.
A fair die is rolled. What is the probability of rolling a 3 or a 4?