Ch 5 A Survey of Probability Concepts

Which of the following is a Subjective Probability?

If you apply for a job after graduation, your chance of getting the job is 83%.

In the Venn diagram shown, what is the Joint Probability?

P(A and B)

Choose the formula that correctly describes the Special Rule of Multiplication.

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

What does it mean when an experiment has a set of events that are collectively exhaustive?

That at least one of the events must occur.

What does a Joint Probability measure?

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

The value given for an Empirical Probability is based on:

the past history of outcomes from the experiment

Which of the following formulas correctly represents the general rule of multiplication for two events?

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

What is the assumption upon which classical probability is based?

That the outcomes of an experiment are equally likely.

How do you calculate classical probability?

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

How is Empirical Probability calculated?

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

Choose the best description of independent events.

The occurrence of one event has no effect on the probability the other will occur.

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.

What is Empirical Probability?

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

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?

.85

What is the answer for P(~A) if P(A) = 0.7?

0.3

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

0.50

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

1

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:

the occurrence of one event does not change the likelihood that the other will occur

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 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.

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

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

In the Venn diagram shown, the area where the circles overlap is P(A and B). What is this area called?

The Joint Probability of A and B

Which of the following is a Conditional Probability?

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

As the number of trials increases, what does the Law of Large Numbers say about the probabilities?

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

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

Study the Venn diagram shown. What is the value of P(E or F)?

0.60 Reason: P(E or F) = 0.40 + 0.30 - 0.10

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

Contingency table

Consider the experiment of rolling a die. The event getting a 2 and which one of the following would be considered mutually exclusive?

Getting a 4

Which one of the following is a characteristic of the classical approach to probability?

Probabilities assume 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)

The events A and B must be mutually exclusive.

A fair die (each side equally likely) with sides numberer 1 to 6 is rolled a large number of times. Which of these predictions can be made using the Law of Large Numbers?

The number 3 will result about 1/6 of the time.

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.

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

False

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 Reason: P(G1 and G2 and G3) = P(G1)P(G2|G1)P(G3|G1 and G2) = 3/6 x 2/5 x 1/4

A particular brand of cell phone case is available in four different styles and each style comes in three colors. How many different cases are available?

12

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

Given the following contingency table, how many conditional probabilities are listed for the second set of branches? Assume 'Movies Attended' is represented as the first stage of the tree diagram.

6 Reason: For each category of 'Movies Attended,' there are two branches (one for each 'Gender').

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?

25%

Given the following contingency table, how many branches go out from the root to the first column? Assume 'Movies Attended' is represented as the first stage of the tree diagram.

3

In a probability experiment, what is an outcome?

A particular result of the experiment.

Choose the statement that best defines the term "experiment" in the context of probability.

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

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.

Which of the following met the requirements for a probability experiment?

Answer a true or false question Roll a die Toss one coin

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.

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

Which of the following met the requirements for an event?

Roll a die and the result is a 2, 4 or 6 Toss one coin and the result is a head Roll a die and the result is a 1

Which of the following statements best describes permutations?

The order is important Any arrangement of r objects selected from a single group of n possible objects

What is the purpose of using selection with replacement?

The probabilities do not change from one trial to another.

A set of events is collectively exhaustive when:

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

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 if the first card is returned to the deck between draws?

1/16 Reason: (1/4)(1/4)=1/16

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

How would you read the formula P(~A)?

The probability of not A.

Which of the following is the best definition of "event" in the context of a probability experiment?

A set of one or more outcomes of an experiment.

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

complement

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

contingency

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

The City Cafe is known for their vegetable plate lunch special that comes with four vegetables, cornbread, and sweet tea. If the four vegetables can be selected from a list of ten vegetables, what formula should be used to determine how many different vegetable plates are there? Assume no vegetable is selected more than once.

Combination Formula (nCr) Reason: This would require the combination formula because we are selecting from one group and order is not important.

Which of the following numbers could represent a probability that an event will occur? Select all that apply.

3/4 .43 probability cannot be greater than one. Percentages can't be greater than 100%. Probabilities are never negative.

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?

35

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?

7/8

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

In the Venn diagram shown, what does the area inside the circle labeled "Event B" represent?

P(B)

Choose the best description of a Joint Probability.

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

Events are Mutually Exclusive when the occurrence of one event means:

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

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

One and only one result of the experiment.

Select the methodology that would result in a Subjective probability.

Weighing the available information and assigning a probability.