Chapter 5 SmartBook

Study the Venn diagram shown. What is the value of P(C or D)?

0.50 Reason: P(C or D) = 0.30 + 0.40 - 0.20

Suppose that P(X)=0.20, P(Y)=0.40, P(Z)=0.25, and the events are mutually exclusive. What is the probability of X, Y, or Z occurring? .02 0 .2 .25 .85

0.85

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

1

A bowl holds three green and three black marbles. Three marbles are selected randomly. What is the probability that all three are green?

1/20 (3/6)(2/5)(1/4) = 1/20

The probability of rolling a one with a die is 1/6. What is the probability of rolling two ones with two dice?

1/36

When you roll a 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.

5/6 Reason: P(~3) = 1 -P(3) = 1 - 1/6

An urn contains two red and three yellow balls. Two balls are selected randomly without replacement. What is the probability that both are yellow? 6/25 1/4 9/25 6/20

6/20 Reason: P(Y1 and Y2) = P(Y1)P(Y2|Y1) = 3/5 x 2/4

When you flip three coins, the probability that they will show three "heads" is 1/8. What is the probability they will not show 3 heads? 1/2 5/8 7/8 3/8

7/8

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 can she distribute them?

70(nCr)(8C4)= 8!/4!(8-4)!

Identical prizes are to be given to two winners from a group of 12 contestants. What counting formula would you use to determine how many ways the prizes could be given out?

Combination formula

The equation P(A) = 1 - P(~A) is know as the ______ rule.

Complement

What is the name of a table, such as the one shown, that shows the relationship between two variables?

Contingency Table

P(A or B)=P(A) + P(B) For this to be true, which one of the following conditions must be met? Event A and event B must not be able to occur at the same time Event A and event B must be the only outcomes that can occur. Event A and event B must share at least one outcome in common.

Event A and event B must not be able to occur at the same time

True or false: If there is any overlap between events, can the events be considered mutually exclusive? T/F

False

Which of the following are true regarding the Special Rule of Addition and the General Rule of Addition? Select all that apply. If the events A and B are collectively exhaustive you can use the Special Rule of Addition. If the events A and B are not mutually exclusive, you can use the General Rule of Addition. If the events A and B are mutually exclusive, you can use the Special Rule of Addition. If P(A and B) > 0 you can use the Special Rule of Addition.

If the events A and B are not mutually exclusive, you can use the General Rule of Addition. If the events A and B are mutually exclusive, you can use the Special Rule of Addition.

The Special Rule of Addition describes how to calculate which of the following probabilities? P(A or B) P(A and B) P(A|B)

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

Which of the following expressions accurately represents the General Rule of Addition?

P(A or B) = P(A) + P(B) - P(A and B)

Which of the following is a Conditional Probability? The chance that a coin will come up 'tails' on the first flip and 'heads' on the second flip. The chance that it will rain today or it will rain tomorrow. The chance a high school student will do well in college given the student scored well on the ACT.

The chance a high school student will do well in college given the student scored well on the ACT.

What does a Joint Probability measure? The probability that at least one or more of a set of events will occur. The likelihood that two or more events will happen at the same time. The likelihood that neither of two events will occur. The probability that one event or the other but not both will occur.

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

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

The occurrence of one event has no effect on the probability the other will occur. Reason: In probability notation A and B are independent if P(A|B)=P(A)

How would you read the formula P(~A)? The approximate probability of A The probability of not A. The probability of A Not the probability of A. The probability of about A.

The probability of not A.

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

The probability that both events will occur is found by multiplying the individual probabilities. Reason: I.e. P(A and B) = P(A)P(B)

0.6 A bowl contains three red and four yellow marbles. You randomly select two marbles from the bowl. Which of the following is a conditional probability? Assume the second marble is drawn from the marbles remaining after the first draw.

The probability that the second marble will be red, if the first one was yellow.

Choose the best description of a Joint Probability. The probability that one event will occur given that the other has already occurred. The probability that two or more events will happen at the same time. The probability that one event will occur and the other won't. The sum of the probabilities of two jointly occurring events.

The probability that two or more events will happen at the same time.

Which of the following met the requirements for a probability experiment? Select all that apply a. Roll a die b. Answer a true or false question c. The ages of patients at a local hospital d. The number of students at a local university e. Toss one coin

a,b,e

Which of the following met the requirements for an event? select all that apply. a. Roll a die and the result is a 2, 4 or 6 b. Roll a die and the result is a 1 c. The number of students at a local university d. The ages of patients at a local hospital e. Toss one coin and the result is a head

a,b,e

Which of the following is a Subjective Probability? a. If you apply for a job after graduation, your chance of getting the job is 83%. b. If you toss three coins the chance of getting all "heads" is one eighth. c. The chance Stephen Curry will make a free throw is 92%.

a. If you apply for a job after graduation, your chance of getting the job is 83%. Reason: this is subjective, because there is no history for your own mortality,

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 recorded 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.

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. a. empirical b. subjective c. classical

a. empirical

Events are Mutually Exclusive when the occurrence of one event means: a. that none of the other events can occur at the same time b. that none of the other events can occur without it c. that the other events will also occur

a. that none of the other events can occur at the same time

Which of the following statements best describes permutations? The order is not important Any arrangement of r objects selected from a single group of n possible objects The order is important Total number of arrangements is equal to m x n

b,c

Consider the experiment of rolling a die. The event getting a 2 and which one of the following would be considered mutually exclusive? a. Getting an even b. Getting a 4 c. Getting a number bigger than 1 d. Getting a number less than 5

b. Getting a 4

Which of the following best describes the meaning of "outcome" in the context of a probability experiment? a. The guaranteed 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.

Which one of the following is a characteristic of the classical approach to probability? a. Probabilities are based on outcomes observed from past experiments. b. Probabilities assume outcomes of an experiment are equally likely. c. Probabilities are based on opinion.

b. Probabilities assume outcomes of an experiment are equally likely.

As the number of trials increases, what does the Law of Large Numbers say about the probabilities? a. The subjective probability will approach the true probability. b. The empirical probability will approach the event's true probability. c. The classical probability will approach the true probability.

b. The empirical probability will approach the event's true 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.

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

b. The relative frequency with which the event happened in the past.

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

b. the past history of outcomes from the experiment

A fair coin (that is, the probability of "heads" equals 50%) is repeated flipped. What does the Law of Large Numbers predict? a. As the number of flips increases, flips will alternate between "heads" and "tails." b. Exactly half the trials will result in "tails". c. As the number of flips increases, the proportion of "heads" will approach 1/2.

c. As the number of flips increases, the proportion of "heads" will approach 1/2.

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

c. That the outcomes of an experiment are equally likely.

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 can occur at the same time. 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 have some outcomes in common.

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

How is Empirical Probability calculated? a. The formula is determined by the individual calculating the probability. b. The number of favorable outcomes divided by the number of possible outcomes. c. The number of times the event occurs divided by the total number of observations.

c. The number of times the event occurs divided by the total number of observations.

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

c. at least one of the events must occur when the experiment is done

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

contingency

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. 20% b. 1/10 c. 2/6 d. 25% e. 8/2

d. 25%

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

d. That at least one of the events must occur.

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?

m x n Reason: This is called the Multiplication Rule.

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

the occurrence of one event does not change the likelyhood that the other will occur Probability notation: P(A|B) = P(A)