Statistics Chapter 5 Practice

Two coins are tossed and the results observed. Match the term to the part of the random trial to which it refers. 1. Experiment 2. Outcome 3. Event a. The process of tossing the coins b. One coin is "heads" and the other "tails". c. One or more coins shows "heads".

1. Experiment=a. The process of tossing the coins 2. Outcome=b. One coin is "heads" and the other "tails". 3. Event=c. One or more coins shows "heads".

Which two of the following numbers could represent a probability that an event will occur? a) -0.3 b) 3/4 c) 1.2 d) .43

b) 3/4 d) .43

The equation P(A) = 1-P(~A) is known as the ________ Rule.

complement

In the context of probability, an experiment is a process: a) that either confirms or denies a hypothetical outcome b) that leads to only one of several possible results c) that has a mathematically predictable result

a) that either confirms or denies a hypothetical outcome b) that leads to only one of several possible results

Two events are mutually exclusive if: a) the occurrence of one event means the other can't occur at the same time b) the occurrence of one of the events means that the other event must also occur c) both events occur to the exclusion of all other events

a) the occurrence of one event means the other can't occur at the same time

Jack wants to pack three different colored shirts for a trip. If he has seven colors to choose from, how many different selections of shirts can he make? a) 210 b) 70 c) 35 d) 21

c) 35

An urn contains two red and three yellow balls. Two balls are selected randomly. What is the probability that both are yellow? a) 9/25 b) 6/25 c) 6/20 d) 1/4

c) 6/20

Mary has tickets to a concert. She wants to give four of them to her friends. If she has eight friends and only gives one ticket to each person, how many different ways she can distribute them? a) 1680 b) 860 c) 70 d) 26

c) 70

Choose the formula that correctly describes the Special Rule of Multiplication. a) P(A and B)=P(A)+P(B) b) P(A x B)=P(A)xP(B) c) P(A and B)=P(A)P(B) d) P(A and B)=P(A)P(B)+P(A or B)

c) P(A and B)=P(A)P(B)

If the order of a set of selected objects is not important, any selection is called a _______.

combination

In the context of Baye's Theorem, which of the following statements best describes a Prior Probability? a) The initial probability based on the present level of knowledge. b) The previously calculated probability that a conditional (dependent) event will occur. c) The probability that additional information will require a revision to a given probability.

a) The initial probability based on the present level of knowledge.

A cubic die with sides numbered 1 to 6 is rolled a large number of times. Which of these predictions can be made using the Law of Large Numbers? a) The number 3 will be uppermost about one sixth of the time. b) Even numbers will occur a large number of times. c) The number 2 will be uppermost more that 1/5th of the time.

a) The number 3 will be uppermost about one sixth of the time.

The formula P(~A) is read as "the probability of __________ A".

not

An event is nearly certain to occur if the probability of it occurring close to _______.

one

If the set of events from an experiment are mutually exclusive and collectively exhaustive, the sum of the probabilities is ___________.

one

If the fraction of times an event happened in the past is used as the basis for assigning a probability to the event, this is _____________ probability.

empirical

Which of the following statements best describes the Law of Large Numbers? a) For a large number of trials, the empirical probability will approach the true probability. b) If you do an experiment a large number of times, the subjective probability will approach the classical probability. c) For a large number of observations the empirical probability will approach the subjective probability.

a) For a large number of trials, the empirical probability will approach the true probability.

A particular brand of e-reader is available in four colors and three different styles. This means that ______ different covers are available.

12

A certain brand of yogurt comes in three sizes and five fruit flavors. Considering all the different sizes and flavors, there are _________ different kinds available.

15

The Complement Rule tells us that P(A)+P(~A)= ___.

one

The general rule of multiplication for two probabilities says that P(A and B)=_______. Choose the formula that correctly fills the blank. a) P(A)P(B) b) P(A)P(B|A) c) P(A)P(B)+P(B|A) d) P(A)P(A|B)

b) P(A)P(B|A)

When you roll a gaming die, the probability that the face with three dots will lie uppermost is 1/6. Use the complement rule to find the probability that the upper face will not be a three. a) 1/2 b) 1/3 c) 4/6 d) 5/6

d) 5/6

Which of the following formulas correctly shows the general rule of multiplication for three events? a) P(A and B and C) = P(A|B|C) b) P(A and B and C)=P(A|B)P(B|C)P(A|C) c) P(A and B and C) = P(A)P(B)P(C) d) P(A and B and C) = P(A)P(B|A)P(C|A and B)

d) P(A and B and C) = P(A)P(B|A)P(C|A and B)

In a random experiment there are 8 possible outcomes, and two of them correspond to a favorable event. What is the classical probability of the event? a) 25% b) 1/10 c) 2/6 d) 20%

a) 25%

When you flip three coins, the probability that they will show three "heads" is 1/8. What is the probability they will show 0, 1, or 2 heads? Hint: use the Complement rule. a) 7/8 b) 1/2 c) 5/8 d) 3/8

a) 7/8

Choose the formula that states the Special Rule of Addition. a) P(A or B)=P(A)+P(B) b) P(A+B)=P(A) or P(B) c) P(A and B)=P(A)+P(B) d) P(A)+P(B)=P(A) or P(B)

a) P(A or B)=P(A)+P(B)

Six runners are doing the 100 meter dash. The winner receives a blue ribbon and the second place runner gets a red ribbon. How many ways can the ribbons be awarded? a) 15 b) 30 c) 12 d) 36

b) 30

What is the purpose of using selection with replacement? a) The probabilities for the second trial change depending on the result of the first trial. b) The empirical probabilities can be calculated more accurately. c) The probabilities do not change from one trial to another. d) The experiment is easier to carry out.

c) The probabilities do not change from one trial to another.

A table used to classify observations according to two or more identifiable characteristics, and often used to determine probabilities is called a __________ table.

contingency

A bowl holds two white and three black marbles. Three marbles are selected randomly. What is the probability that all three are black? a) 4/30 b) 9/125 c) 3/5 d) 1/10

d) 1/10

The chance of drawing a spade from a deck of cards is 1/4. If the deck is shuffled between draws, what is the probability of drawing two spades in two draws? a) 1/2 b) 1/4 c) 2/16 d) 1/16

d) 1/16

As the number of trials increases, what does the Law of Large Numbers say about the probabilities? a) The subjective probability will approach the classical probability. b) The empirical probability will approach the classical probability. c) The number of favorable outcomes will become larger.

b) The empirical probability will approach the classical probability.

How do you calculate classical probability? a) Number of actual outcomes divided by the number of possible outcomes. b) The number of favorable outcomes divided by the number of possible outcomes. c) The number of events divided by the number of possible outcomes.

b) The number of favorable outcomes divided by the number of possible outcomes.

Two events are independent if: a) the occurrence of one event precludes the occurrence of the other event. b) the occurrence of one event does not change the likelihood that the other will occur. c) either event can occur with or without the other.

b) the occurrence of one event does not change the likelihood that the other will occur. c) either event can occur with or without the other.

Which of the following is the best definition of "event" in the context of a probability experiment? a) A particular outcome of a random experiment b) The process of performing a random experiment c) A set of one or more outcomes of an experiment

c) A set of one or more outcomes of an experiment

From the following statements, choose two that are characteristics of contingency tables. a) It shows only conditional probabilities. b) It shows the dependent variable on the horizontal axis. c) It can use nominal data. d) It has a two way table frequently used to determine various probabilities.

c) It can use nominal data. d) It has a two way table frequently used to determine various probabilities.

For three mutually exclusive events, A, B, and C, what is P(A or B or C)? This is the special rule of addition for three events. a) P(A+B+C) b) P(A and B)+P(A and C) c) P(A)+P(B)+P(C) d) P(A or B)+P(B or C)

c) P(A)+P(B)+P(C)

In the context of Baye's Theorem, which of the following statements best describes the Posterior Probability? a) The last conditional probability to appear in the formula for Baye's Theorem. b) A revised probability based on additional information. c) The probability that a subsequent event will occur requiring a revision to the Prior Probability.

b) A revised probability based on additional information.

Which two of the following statements describe a probability? a) It is always expressed as a percentage b) It describes the relative likelihood that an event will occur c) It is a number between 0 and 1 inclusive d) A probability lies between minus one and plus one

b) It describes the relative likelihood that an event will occur c) It is a number between 0 and 1 inclusive

Which of the following best describes the meaning of "outcome" in the context of a probability experiment? a) The expected result of the experiment. b) One and only one result of the experiment. c) Anything that can happen as a result of the experiment.

b) One and only one result of the experiment.

A random experiment consists of tossing two coins. Which of the following is not an event for this experiment. a) One coin comes up "heads". b) One of the coins is lost under the table. c) One coin comes up "heads" and the other "tails". d) Both coins come up "tails".

b) One of the coins is lost under the table.

What does it mean when an experiment has a set of events that are collectively exhaustive? a) That all of the events will occur. b) That the experimenter will be very tired. c) That at least one of the events must occur. d) That only one of the events can occur as a result of the experiment.

c) That at least one of the events must occur.

Which one of the following conditions must be met to use the Special Rule of Addition? I.e. P(A or B)=P(A)+P(B) a) Events A and B have some outcomes in common. b) The events A and B must be collectively exhaustive. c) The events A and B must be mutually exclusive. d) Events A and B can occur at the same time.

c) The events A and B must be mutually exclusive.

What is the assumption upon which classical probability is based? a) That the outcomes of an experiment are equally likely. b) That all events are equally likely. c) That events are made up of more than one outcomes. d) That the number events is less than the number of outcomes.

a) That the outcomes of an experiment are equally likely.

Which of the following is a Conditional Probability? a) The chance that you will take the short straw, given that two people before you drew long straws. b) The chance that a coin will come up "tails" given that it was heads the previous five times. c) The chance that it will rain, given that you just washed your car.

a) The chance that you will take the short straw, given that two people before you drew long straws.

What does a Joint Probability measure? a) The probability that one event or the other but not both will occur. b) The probability that one or more of a set of events will occur concurrently. c) The likelihood that either of two events will occur. d) The likelihood that two or more events will happen at the same time.

d) The likelihood that two or more events will happen at the same time.

A set of events is collectively exhaustive when: a) the occurrence of one event means that the other cannot occur b) the occurrence of one of the events means that the other must occur c) all of the events must occur when the experiment is done d) at least one of the events must occur when the experiment is done

d) at least one of the events must occur when the experiment is done

What determines whether you use the Special Rule of Addition or the General Rule of Addition to find the value of P(A or B)? a) If the events A and B are mutually exclusive, you can use the Special Rule of Addition. b) If P(A and B)>0 you can use the Special Rule of Addition. c) If the events A and B are collectively exhaustive you can use the Special Rule of Addition

a) If the events A and B are mutually exclusive, you can use the Special Rule of Addition.

Choose the statement that best defines the term "experiment" in the context of probability. a) A process that leads to only one of several possible outcomes. b) A random trial whose outcome can be predicted on the basis of mathematical analysis. c) A process that may or may not confirm a hypothesis.

a) A process that leads to only one of several possible outcomes.

Which of the following statements best describes the purpose of Baye's Theorem? a) It allows us to use new information to revise previous probabilities. b) It allows us to combine prior probabilities to obtain a posterior probability. c) It lets us calculate conditional probabilities for independent events.

a) It allows us to use new information to revise previous probabilities.

Which of the following formulas correctly represents the general rule of multiplication for two events? a) P(A and B) = P(A)P(B|A) b) P(A and B) = P(A)+P(B)-P(A|B) c) P(A and B)=P(A)P(B) d) P(A and B) = P(A|B)

a) P(A and B) = P(A)P(B|A)

Choose two of the following statements that describe the data commonly displayed in a contingency table. a) The data summarizes two variables of interest and their relationship. b) The data gathered results from the performance of a random experiment. c) The data can be of nominal level. d) The data is never of ordinal level, i.e. arranged in rank order.

a) The data summarizes two variables of interest and their relationship. c) The data can be of nominal level.

A fair coin (that is, the probability of "heads" equals 50%) is flipped one thousand times. What does the Law of Large Numbers predict? a) The number of "heads" will be 500. b) The proportion of "heads" will be close to 1/2. c) Exactly half the trials will result in "tails".

a) The number of "heads" will be 500. b) The proportion of "heads" will be close to 1/2.

Which of the following statements accurately repeats the formula P(B)=0.30? a) The probability that the event "B" will occur is thirty percent. b) P times B equals zero point three. c) The Bernoulli probability is 30%. d) The function "P" of the variable "B" equals 0.3.

a) The probability that the event "B" will occur is thirty percent.

Which of the following is a Subjective Probability? a) If you are a non-smoker, your chance of dying of heart failure is 22%. b) The S&P 500 index has a 27% chance of increasing by more than 10% this year. c) If you toss three coins the chance of getting all "heads" is one eighth.

a) If you are a non-smoker, your chance of dying of heart failure is 22%.

For two independent events, which statement correctly describes the Special Rule of Multiplication? a) The probability that both events will occur is found by multiplying the individual probabilities. b) The probability that the events will occur together is the sum of the individual probabilities. c) The probability that both events will occur is the product of the probabilities plus the probability that one or the other will occur.

a) The probability that both events will occur is found by multiplying the individual probabilities.

What is Empirical Probability? a) The relative frequency with which the event happened in the past. b) The likelihood of an event that is suggested by an individual. c) The ratio of favorable outcomes to possible outcomes.

a) The relative frequency with which the event happened in the past.

In a probability experiment, what is an outcome? a) The set of all possible results of the experiment. b) The result that was predicted beforehand. c) A particular result of the experiment.

a) The set of all possible results of the experiment. c) A particular result of the experiment.

An urn contains three black and two white beans. Which of the following experiments represents selection without replacement? a) Three beans are taken from the urn one at a time and their colors noted. b) Three beans are taken from the urn, their colors noted, then put back in the urn. c) A bean is selected, its color noted, and returned to the urn. This is done three times. d) Two beans are taken from the urn, then returned one at a time.

a) Three beans are taken from the urn one at a time and their colors noted.

The value given for an Empirical Probability is based on: a) the past history of outcomes from the experiment b) someone's "best guess" based on his knowledge of the situation c) the ratio of favorable outcomes to possible outcomes to the experiment

a) the past history of outcomes from the experiment

Choose the best description of independent events. a) The occurrence of one event means that the other event must not occur. b) The occurrence of one event has no effect on the probability the other will occur. c) One event can occur whether or not the other events occurs.

b) The occurrence of one event has no effect on the probability the other will occur. c) One event can occur whether or not the other events occurs.

Select the methodology that would result in a Subjective probability. a) Weighing the available information and assigning a probability. b) Counting the number of favorable outcomes and dividing by the record-able total number of outcomes. c) Dividing the number of favorable events by the number of possible events.

a) Weighing the available information and assigning a probability.

A first place, second place, and a third place winner will be selected from 8 persons who entered a contest. How many ways can the prized be given out? a) 21 b) 56 c) 512 d) 336

d) 336

If there are m ways of doing one thing and n ways of doing another, how many ways are there to do both? For example, if a toy comes in m colors and n sizes, how many different toys can there be? a) m+n b) m(n-1) c) m^n d) m x n

d) m x n