Deck 5: Introduction to Probability

Question 1

If an experiment has only two unique possible outcomes, then the probability of getting one of those two outcomes is 0.5.

Answer 1

True

Question 2

Suppose there are seven jelly beans in a bowl-three red and four blue. If a jelly bean is selected at random, what is the probability that it is blue?

A)2/7
B)3/7
C)4/7
D)5/7

Answer 2

C

Question 3

ABC College is using a new screening test to test its employees for TB. The following table shows the results of a pilot study: Assuming that this result is representative of the college, estimate the probability that a randomly chosen employee who tested positive has TB.

A)89.1%
B)84.0%
C)13.3%
D)61.8%

Answer 3

D

Question 4

The _____ of a test is the probability that the test will give a negative result for a person who does not have the disease.

A)specificity
B)sensitivity
C)false positive
D)true negative

Question 5

Suppose the inside bottom of a box is painted with three colors: one-third of the bottom area is blue, one-sixth is red, and one-half is yellow. If you toss a tiny pebble into the box without aiming, what is the probability the pebble will NOT land on the color blue?

A)2/3
B)1/3
C)5/6
D)1/2

Question 6

_____ probability is the probability that one event occurs given that another has occurred.

A)Recurrent
B)Disjunctive
C)Conditional
D)Predictive

Question 7

ABC College is using a new screening test to test its employees for TB. The following table shows the results of a pilot study: What percentage of the individuals in the study were false negatives?

A)75.9%
B)2.5%
C)13.3%
D)8.2%

Question 8

ABC College is using a new screening test to test its employees for TB. The following table shows the results of a pilot study: For what percentage of the individuals in the study did the test return an INCORRECT result?

A)89.1%
B)34.0%
C)15.8%
D)10.8%

Question 9

Suppose you pick a marble from a box containing five red and seven blue marbles. You record the color and put the marble back in the box. What is the probability of getting a red marble both times if you do this twice?

A)5/12
B)4/11
C)25/144
D)5/33

Question 10

If an event can never occur, then the probability of the event is:

A)-1
B)0
C)0.5
D)1

Question 11

A friend claims that it will rain today with probability 30% and tomorrow with probability four times as great as today. Which of the following is CORRECT?

A)The claim can be true because it is more likely to rain tomorrow if we have rain today.
B)The claim cannot be true because raining tomorrow is not guaranteed.
C)The claim can be true because it is possible to have rain tomorrow.
D)The claim cannot be true because any probability is between 0 and 1.

Question 12

The prevalence of a disease in a given population is the percentage of the population that does NOT have the disease.

Question 13

ABC College is using a new screening test to test its employees for TB. The following table shows the results of a pilot study: What percentage of the individuals in the study who had TB tested negative?

A)3.2%
B)2.5%
C)16.0%
D)8.0%

Question 14

Michael and Surrey are planning to have three children. Assuming it is equally likely for a boy or a girl to be born, what is the probability that at least one of their children will be a boy?

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

Question 15

The probability of passing Professor Avila's math class is 65%, the probability of passing Professor Reid's biology class is 45%, and the probability of passing both is 25%. What is the probability of passing one or the other?

A)75%
B)85%
C)70%
D)110%

Question 16

A city study finds that the probability of a car running a red light at a certain intersection during any given day is 9.6%. What is the probability that a car will NOT run the red light on a given day?

A)8.6%
B)96.0%
C)4.0%
D)90.4%

Question 17

If each outcome of an experiment is equally likely, the _____ of an event is a fraction of favorable outcomes.

A)chances
B)odds
C)probability
D)success

Question 18

Suppose a coin is tossed three times and we count the total number of heads. How many possible outcomes are there?

A)3
B)4
C)5
D)6

Question 19

The _____ of a test is the probability that the test will detect the disease in a person who does have the disease.

A)specificity
B)sensitivity
C)false positive
D)true negative

Question 20

Suppose there are 15 jelly beans in a bowl-3 green, 5 blue, and 7 red. A jelly bean is selected at random. What is the probability the jelly bean is NOT blue?

A)1/3
B)2/3
C)7/15
D)8/15

Question 21

How many outcomes are possible if we toss a coin 10 times?

A)20
B)256
C)512
D)1024

Question 22

You toss a coin and then roll a die. What is the probability that you get a head followed by a 4?

A)1/4
B)5/12
C)1/12
D)1/2

Question 23

Two events, A and B, are independent exactly when P(A or
B) = P(A) + P(B).

A)True
B)False

Question 24

A shirt company has three designs that can be made with either short or long sleeves. There are six colors available. How many different types of shirts are available?

A)11
B)18
C)24
D)36

Question 25

The area of the Unites States is 3.79 million square miles, and Alaska covers 0.59 million square miles. Suppose a meteorite falls from the sky and strikes Earth. What is the probability the meteorite strikes Alaska given it strikes the United States?

A)15.6%
B)5.9%
C)37.9%
D)22.4%

Question 26

Suppose you toss a pair of dice. What is the probability that the total number of dots appearing is greater than 7?

A)1/4
B)1/3
C)5/12
D)7/12

Question 27

You roll a die twice. The event of getting an even number on the first roll and another event of getting an odd number on the second roll are independent.

Question 28

You toss a coin three times. What is the probability of getting three heads?

A)1/2
B)1/3
C)1/6
D)1/8

Question 29

In a standard deck of cards, the jack, queen, and king are called face cards. If you randomly choose a card from the deck, what is the probability that it is a jack or queen given that it is a face card?

A)1/3
B)2/3
C)10/13
D)3/52

Question 30

You are voting in a state election. There are three candidates for governor, five candidates for lieutenant governor, four candidates for the state house of representatives, and two candidates for senator. How many different ways could you fill out the ballot if you vote once for each office?

A)14
B)60
C)64
D)120

Question 31

A bag contains three red cubes, two blue cubes, four red balls, and three blue balls. When you draw a ball at random, what is the probability that the color is blue?

A)5/12
B)3/7
C)2/5
D)3/12

Question 32

Susan bakes 10 chocolate chip and 10 peanut butter cookies. Will bakes 6 chocolate chip and 12 peanut butter cookies. The 38 cookies are put together and offered on a single plate. If you select a cookie from the plate at random, what is the probability that the cookie is peanut butter, given that Will baked it?

A)5/8
B)11/19
C)6/19
D)2/3

Question 33

The following table gives the results of a screening test for a disease: Estimate the specificity of the test.

A)69.2%
B)72.0%
C)32.0%
D)53.3%

Question 34

Suppose you toss a pair of dice. What is the probability that the total number of dots appearing is 6?

A)5/6
B)5/36
C)1/6
D)25/36

Question 35

Suppose you randomly choose two cards from a thoroughly shuffled deck. If you put the first card back in the deck before you draw the second, what is the probability that the first card is an ace and the second card is a king?

A)2/13
B)1/169
C)1/221
D)3/676

Question 36

The following table gives the results of a screening test for a disease: Estimate the sensitivity of the test.

A)18.5%
B)80.6%
C)23.7%
D)53.3%

Question 37

A shoe store sells one brand of shoe in five styles, six sizes, and three colors. How many different types of shoes are available?

A)33
B)90
C)14
D)150

Question 38

Suppose you randomly choose two cards from a thoroughly shuffled deck. If you do NOT put the first card back in the deck before you draw the second, what is the probability that the first card is club and the second card is a spade?

A)13/204
B)2/51
C)1/16
D)1/17

Question 39

Two experiments are _____ if knowing that one event occurs has no effect on the probability of the occurrence of the other.

A)dependent
B)independent
C)inclusive
D)exclusive

Question 40

The telephone numbers in a small town either begin 373 or 377. How many telephone numbers are available?

A)10,000
B)20,000
C)30,000
D)40,000

Question 41

You draw three cards from a full deck without jokers. What is the probability that they will all be clubs?

A)0.017
B)0.013
C)0.016
D)0.012

Question 42

A teacher keeps track of the number of absences in a class each day along with their probabilities. Her results are in this table: What is the expected number of absences for any given day?

A)1.8
B)2.3
C)3.2
D)3.8

Question 43

Suppose there is a group of nine people from whom we will make a committee. In how many ways could a four-person committee be selected?

A)3024
B)36
C)24
D)126

Question 44

A candy jar has 12 different pieces of candy in it. If you want to select 2 pieces, how many choices do you have?

A)66
B)132
C)24
D)23

Question 45

You draw five cards from a full deck without jokers. What is the probability that you have at least one face card (jack, queen, or king)?

A)45.9%
B)65.8%
C)74.7%
D)82.9%

Question 46

An ice cream parlor sells 10 flavors. If you'd like a bowl with three scoops, each a different flavor, how many choices do you have?

A)720
B)120
C)60
D)30

Question 47

A _____ of a group of items is a selection from that group in which order is not taken into account.

A)combination
B)listing
C)permutation
D)sequence

Question 48

For a game, the average amount you can expect to win (or lose) per play in the long run can be measured by:

A)standard value.
B)winning wager.
C)expected value.
D)value at risk.

Question 49

If a license plate uses a three-digit number followed by three letters of the English alphabet, how many license plates can be made?

A)17,576,000
B)15,818,400
C)14,040,000
D)11,232,000

Question 50

A _____ of items is an arrangement of the items in a certain order.

A)combination
B)listing
C)permutation
D)sequence

Question 51

Bob and Will toss two coins. If both coins come up heads, Bob pays Will $6. Will pays Bob $2 otherwise. What is the expected value of this game for Bob?

A)$0.25
B)$0.50
C)$0.00
D)$4.00

Question 52

The total number of ways to arrange n distinct items without repetition is:

A).
B)
C).
D).

Question 53

An economist estimates that casinos in California net $6 billion each year. Assume that overall the casinos take in 4.25% of the money wagered. How much money was bet in California last year?

A)$141 billion
B)$26 billion
C)$71 billion
D)$165 billion

Question 54

A game is said to be fair if the expected value is:

A)positive.
B)negative.
C)large.
D)zero.

Question 55

We have a box with six green marbles, five blue marbles, and seven red marbles. We choose three marbles from the box at random without looking. What is the probability that they will all be blue?

A)0.010
B)0.026
C)0.021
D)0.012

Question 56

We have a box with six green marbles, five blue marbles, and seven red marbles. We choose three marbles from the box at random without looking. What is the probability that none of them will be blue?

A)0.38
B)0.29
C)0.45
D)0.35

Question 57

Seven horses are running in a race. In how many ways can we have first-, second-, and third-place finishers, assuming there are no ties?

A)35
B)210
C)10
D)6

Question 58

You draw three cards from a full deck without jokers. What is the probability that they will all be face cards (jacks, queens, or kings)?

A)0.010
B)0.013
C)0.012
D)0.009

Question 59

There are seven candidates running for the presidential and vice-presidential nomination. How many different ways are there of selecting presidential and vice-presidential candidates from the field?

A)14
B)13
C)49
D)42

Question 60

The _____ is the belief that a string of losses in the past will be compensated by wins in the future.

A)law of large numbers
B)gambler's bet
C)gambler's fallacy
D)winning wager

Question 61

In a dice game, you win if the two dice come up 10 or higher. Otherwise, you lose $1. What should be the profit for winning to make this game fair?

A)$4
B)$5
C)$6
D)$7

Question 62

Suppose you decide to open a casino offering only one game. You win a dollar 55% of the time, and your customer wins a dollar 45% of the time. How much profit would you expect to have if 7500 games are played?

A)$500
B)$750
C)$1000
D)$1250

Question 63

You are playing a card game using a full deck without jokers. If you select a face card (jack, queen, or king), you win $6; otherwise, you lose $3. What is the expected value for this game?

A)-$0.92
B)$0.92
C)-$3.69
D)$3.69

Question 64

What is your expected value for a game if your probability of winning is 1/5 and your profit is three times your wager? Assume the wager is $1.

A)$0.20
B)-$0.20
C)-$1.40
D)$1.40

Question 65

What is your expected value of winning for a game whose probabilities and outcomes are given in the following table? Assume the wager is $1.

A)$1.30
B)-$1.30
C)$0.10
D)-$0.10

Question 66

Each question on a multiple-choice exam has four choices. One of the choices is correct, worth four points. Another choice is wrong but carries partial credit of one point. The other two choices are wrong and worth negative one point. If a student picks answers at random, what is the expected value of his or her score for a problem?

A)0.25
B)1.25
C)0.75
D)1.50

Question 67

You play a gambling game with a friend in which you win 25% of the time and lose 75% of the time. When you lose, you lose $1. What profit should you earn when you win, in order for the game to be fair?

A)$1
B)$2
C)$3
D)$4

Question 68

You roll a pair of dice. You bet $1 that you will get 2, 3, or 12. If you win, you are paid $9, for a profit of $8; if you lose, you lose your wager. This is a fair game.