Chapter 5 Probability

Two outcomes (A and B) are independent, where p(A) = .45 and p(B) is .28. What is the probability of A and B?

.45 x .28= .126 = .13

The probabilities for two outcomes are ____________ when the sum of their probabilities is equal to 1.00( 100%). The outcomes of two events are exhaustive because they will always add up to 1.00.

Complementary

Does p(A)+p(B)=1.00 demonstrates complementary or mutually exclusive outcomes?

Complementary outcomes

The probabilities for two outcomes are ____________ when the probability of one outcome is dependent on the occurrence of the other outcome.

Conditional

The probability of an outcome is particularly useful for predicting the likelihood of fixed events. True/False

False

Symbolically, the probability of two mutually exclusive outcomes of A and B can be represented as:

p(A ∩ B)=0 symbol in the middle can be referred to as an intersection

The multiplicative rule can be stated as p(A∩ B) = _____________________

p(A) x p(B)

Each probability in a probability distribution ranges between ______ and _____; and can never be negative

0 and 1

Suppose that the probability that any child of alcoholic parents becomes alcoholic is p = .16. Assuming independent outcomes, the probability that two children of alcoholic parents will be alcoholic equals

0.025 rounded to .03(use multiplicative rule)

The probability that someone in the human population has blood type AB is about p = .08; the probability that someone has blood type O is about p = .25. Knowing that each individual can have one and only one blood type, what is the probability that a person has an AB or O blood type?

0.33 (use additive rule)

The sum of probabilities in a probability distribution is equal to ∑p(x)=

1.00

A news poll showed that voters had no preference for either of three candidates. In this example, the probability of a vote for, say, Candidate A equals

1/3

A gambler rolls a 3 with one roll of a single fair die. Given that the die was six-sided, what was the probability of rolling a 3 with one roll?

1/6

The following are six random outcomes for a sample space: -1, -3, -3, -2, -5, and -6. What is the probability of selecting a -3 in this example?

2/6

Assuming the outcomes are complementary, if the the probability of dying during bypass surgery is 5%, whats the probability of surviving?

95% because 1-.05=.95

A)Random B)un-random event is any event in which the outcomes observed can vary

A) Random

Which rule states that when two outcomes are mutually exclusive, the probability that either one of these outcomes will occur is the sum of their individual probabilities?

Additive Rule

For Mutually Exclusive outcomes you can calculate the that one or another outcome occurs by using the ______________ rule

Additive Rule symbol in the middle can be called an "or"

The alternative formula for conditional probabilities is known as ________________ Theorem

Bayes

Each of the following is an example of a binomial distribution, except A) the number of heads in ten flips B) the number of males and females in a sample C) the number of votes for or against a candidate D) the time it takes to complete a driving test

D) the time it takes to complete a driving test

The mean of a probability distribution is called the

Expected Value of the mean and mathematical expectation

The probabilities for two outcomes are __________ when the probability of one outcome does not affect the probability of the second outcome.

Independent

When two outcomes (A and B) are independent, the probability that both outcomes occur is equal to the product of their individual probabilities. This is called the _______________ rule

Multiplicative

In one flip of a fair coin, it is not possible to flip heads AND tails at the same time. This is an example of a ________________ outcomes

Mutually exclusive

The probabilities for two outcomes are _________________ when two outcomes cannot occur together. The probability of them occurring together is 0

Mutually exclusive

Four relationships that can exist between two outcomes

Mutually exclusive, independent, complementary, and conditional

P________________ is used to describe the likelihood that an outcome will occur.

Probability

The proportion or fraction of times an outcome is likely to occur is referred to as

Probability

The distribution of probabilities for each outcome of a random variable that sums to 1.00 is called a

Probability Distribution

A ___________ variable can be measured or obtained from a random experiment. Unlike other mathematical variables, it is NOT the actual outcome of a random experiment but rather describes the possible, as yet undetermined outcomes in an experiment

Random

To calculate probability need to know two things:

Sample Space= total number of possible outcomes that can occur in a given random event and How often an outcome of interest occurs

The formula for probability is............ " p(x)=f(x) /sample space

The formula for probability is the frequency of times an outcome occurs, f(x), DIVIDED by the sample space(total number of outcomes)

In the behavioral sciences, it is often necessary to compute the probability of two or more outcomes for a given event: T/F

True

Probability is unnecessary in a fixed event T/F

True

Probability ranges between 0 and 1 and is never negative. True/False

True

T/F: The probability formula looks very familiar to calculation of relative frequency and its because relative frequency of an event IS the probability of its occurrence.

True

The sample space is equal to the total number of random outcomes possible for a random variable. True/False

True

Because the sum of probabilities for two complementary outcomes is equal to 1.00, it is also true that subtracting 1 from the probability of one outcome will equal the probability of the second outcome. T/F

True p(A)=1-p(B) or p(B)=1-p(A)

A professor records the grades for his class of students. He finds that the probability that a student earns an A is p = .14; earns a B is p = .36; earns a C is p = .32; earns a D is p = .10; and earns an F is p = .08. What is the probability that a student earns a B or better in this class?

Using the Additive Rule p(A)+p(B)= .50 that a student earns a B or better in this class

By definition, p_________ is the frequency of times an outcome occurs divided by the total number of possible outcomes

probability

Mean/ Expected Value of a Probability Distribution

μ=∑ (xp)