Psyc 277 Ch 9

Which value below could not be a probability? .54 0 .12 -.12

-.12

85% of the students at a certain community college have graduated. 35% of those graduates go on to complete bachelor's degrees. What is the probability that a student drawn at random will complete a bachelor's degree?

.2975

A "sure thing" would have a probability equal to

1.00

The access code for a security door consists of four digits. Each digit can be any number from 0 through 9. How many access codes are possible?

10,000.00

In the sample space for the probability experiment of rolling a pair of dice, how many outcomes are there?

36.0

The probability experiment of rolling a single die to see if a number greater than 2 comes up has how many outcomes?

4.0

Identify the true statement. A. Events that are not mutually exclusive are also not complementary B. Events with shared elements are mutually exclusive C. Mutually exclusive events are also not complementary D. Dependent events are also not mutually exclusive

A

According to data from the American Cancer Society, about 1 in 3 women living in the U.S. will have some form of cancer during their lives. If three women are randomly selected, what is the probability that they will all contract cancer at some point during their lives? A. 1/81 B. 1/27 C. 1/3

B.

The events getting an A in statistics and getting a C in statistics are A. Complementary events B. Mutually exclusive and dependent C. Mutually exclusive and independent D. Not mutually exclusive

C

Which of the following is not a probability experiment? A. Wagering on the outcome of a spin of a roulette wheel B. Guessing the answer to a multiple choice quiz question C. A soccer player attempting a goal D. Selecting a square on the office football pool

C

Which example would not be defined as trial? A. In the die rolling experiment, one roll of the die represents one trial. B. In the first coin toss experiment, the the coin toss represents one trial. C. In the first coin toss experiment, the result of that toss represents the outcome. There are two possible outcomes, H or T. D. In the second coin toss experiment, the series of four tosses represents one trial.

C. In the first coin toss experiment, the result of that toss represents the outcome. There are two possible outcomes, H or T.

Two ________ events, when combined, make up the entire sample space.

Complementary

Which of the following is a non-example of probability experiment? A. A die is rolled once to see if the number four comes up (probability 1 out of 6, or approximately .167). B. A coin is tossed to see if a heads occurs (probability 1 out of 2, or .5). C. A coin is tossed four times to measure how many heads come up (probability 1 out of 2 to the 4th power, or (.5)4). D. A person buys a raffle ticket

D. A person buys a raffle ticket

In a probability experiment, the set of all possible outcomes represents the sample space. A subset of those outcomes represents a(n) .

Event

Dependent Events

If two events are dependent, the probability that one will occur is affected (changed) by the occurrence of the other.

Independent Events

If two events are independent, the probability that one will occur is not affected by whether or not the other has occurred.

Example of a Set

In the die rolling experiment, the set of all possible outcomes of that trial is represented as {1, 2, 3, 4, 5, 6}, since any number from 1 - 6 is a possible outcome. Each number from 1 to 6 is an element of the set.

Being a dog or a cat are independent events that are also __________. A pet cannot be both a dog and a cat at the same time.

Mutually exclusive

In another group of students, there are 30 juniors and 35 seniors. At least in terms of class ranking, there are no shared elements, so these categories are

Mutually exclusive

Selecting a queen from a card deck, not replacing it, and then selecting a king are dependent events that are

Mutually exclusive

In a group of students, 40 are juniors, 50 are English majors,and 22 are English-major juniors. The 22 English juniors represent elements shared by the two categories "juniors" and "English majors" and could be represented graphically as the intersection of those categories. Since the categories have shared elements, they are

Not mutually exclusive

Probability is key to assessing .

Risk

All possible outcomes of the coin toss experiment can also be summarized in a chart of the sample space as:

S = {(HHHH), (HHHT), (HHTH), (HTHH), (THHH), (HHTT), (HTTH), (HTHT), (TTHH), (THHT), (THTH), (TTTH), (TTHT), (THTT), (TTTH), (TTTT)}

What is a Set?

Set notation is used in probability to describe collections of objects or values that have been defined according to a rule or statement.

In a probability experiment involving the roll of a die, the event "rolling a number greater than five" is a ________ event.

Simple

Regardless of the complexity, all probability experiments have three things in common:

The experiment must have more than one possible outcome • Each possible outcome can be specified in advance • The outcome of the experiment is due to chance

The Fundamental Counting Principle

a mathematical rule that enables us to find the number of ways a combination or series of independent events can occur.

What is a Trial?

can be defined as a single performance of a probability experiment.

What is a Probability Experiment?

can be defined as a situation involving chance or probability that leads to observable and measureable results called outcomes.

What is Probability?

can be defined as the likelihood of an event expressed in numerical terms as a fraction, decimal, or percent.

The addition rule

can be used to find the probability that at least one of two events will occur

The multiplication rule

can be used to find the probability that two (or more) events occur in sequence, and takes the fundamental counting principle a step further by taking into account both independent and dependent events.

A simple event

consists of a single outcome.

A compound event

consists of more than one outcome.

What is an Event?

is a subset of the sample space, which in turn is a collection of all possible outcomes of a probability experiment.

Theoretical probability, or classical probability

is based on a theoretical assumption about the nature of the event, in which it is assumed that n events are equally likely to occur. For example, the theoretical probability of rolling a two on a six-sided die is one sixth.

Subjective Probability

is based on an individual's personal belief about the likelihood of an event occurring.

Empirical probability, or relative frequency probability

is based on the observed outcomes of one or a series of trials. It is the type used most often in statistical inference procedures. For example, a die is rolled 10 times and the number two comes up two times, making the relative frequency 2/10.

What is a Sample Space?

is the description of all possible outcomes of a probability experiment.

What is an Outcome?

is the result of a single trial of a probability experiment.

A die is rolled once to see if the number four comes up. The roll of the die represents one trial. The result of that roll of the die represents the

outcome

One marble is drawn from a jar containing 4 red, 6 blue, and 7 green marbles. What is the sample space?

red, blue, green

A non example of a probability experiment is

something that has only one possible outcome, or for which the possible outcomes cannot be specified in advance, or the outcomes are not due to chance.

Two events are not mutually exclusive if

they can occur at the same time.

Mutually Exclusive Events

they cannot occur at the same time. They could be either dependent or independent.

Examples of an Outcome

• In the die rolling experiment, the result of that roll of the die represents the outcome.There are six possible outcomes, 1 through 6. • In the first coin toss experiment, the result of that toss represents the outcome. There are two possible outcomes, H or T. • In the second coin toss experiment, the result of one series of tosses represents the outcome of that trial. There are 16 possible outcomes, shown in the examples below.

There are three types of events in probability experiments that we need to know about. They are:

• Independent events • Dependent events • Mutually exclusive events

There are three ways to arrive at a probability statement, each based on an approach to the probability in question. They are:

• Theoretical probability • Empirical probability • Subjective probability