If E and F are not disjoint events, then P(E or F)equals=

P(E) + P(F) - P(E and F)

Suppose an experiment consists of rolling a fair die ten times and recording the number of sevens obtained. If event E is defined as getting at least one 7, how would you describe the complement ofE?

The complement of event E is the event that no sevens are obtained.

Three cards are drawn without replacement from a standard deck, and the number of kings is noted. Does this constitute a binomial experiment? Why or why not?

No, because the probability of getting a king is not the same for each of the three draws.

any collection of outcomes from a probability experiment.

event

The probability of obtaining x successes in n independent trials of a binomial experiment is given by P(x)equals=Subscript n Baseline Upper C Subscript x Baseline p Superscript x Baseline left parenthesis 1 minus p right parenthesis Superscript n minus xnCxpx(1−p)n−x, where p is the probability of success. *What does the n−x represent in theformula?

the number of failures

Suppose a fair die is rolled ten times and the result is recorded each time. Does this constitute a binomial experiment?

No, because there are more than two outcomes for each trial.

Three cards are drawn with replacement from a standard deck, and the number of kings is noted. Does this constitute a binomial experiment?

Yes, because there are three independent draws. For each draw there are two outcomes(king and not king) and a constant probability of getting a king.

random variable has either a finite or countable number of values

discrete

If E represents any event and Upper E Superscript cEc represents the complement of E, then Upper P left parenthesis Upper E Superscript c right parenthesis equalsPEc=

1-P(E)

Twenty percent of adults in a particular community have at least a bachelor's degree. Suppose x is a binomial random variable that counts the number of adults with at least a bachelor's degree in a random sample of 100 adults from the community. Which of the following probability statements indicates the probability that at least 30 adults have at least a bachelor's degree?

P(x greater than or equal to 30)

Use symbols to describe the event that a college student is female or has financial aid.

AUB

Two events E and F are __________ if the occurrence of event E in a probability experiment does not affect the probability of event F.

independent

Consider the binomial probability distribution function Upper P left parenthesis x right parenthesis equals StartFraction 25 exclamation mark Over x exclamation mark left parenthesis 25 minus x right parenthesis exclamation mark EndFraction 0.6 Superscript x Baseline 0.4 Superscript 25 minus xP(x)=25!x!(25−x)!0.6x0.425−x. What is the probability of success?

0.6

The Addition Rule P(E or F)=P(E)+P(F) applies only to which type of events?

disjoint

Determine whether the distribution is a discrete probability distribution

No, because the probabilities do not sum to 1.

The notation __________ is used for the binomial random variable which counts the number of successes in n independent trials of an experiment.

x

is a numerical measure of the outcome of a probability experiment

random variable

of a probability experiment is the collection of all possible outcomes

sample space

is used for the number of trials in a binomial experiment.

n

Suppose that in a certain community, the probability of a randomly selected individual having red hair is 0.08 and the probability of a randomly selected individual being left-handed is 0.15. What additional information would be needed to find the probability of randomly selecting an individual in this community who has red hair or is left-handed?

We would need to know the percentage of individuals in the community who have red hair and are left-handed.

Use symbols to describe the event that a college student is female and has financial aid.

A (upsidown U) B

If a sample of 100 people is chosen from a town of 100,000 people without replacement, is it reasonable to assume that events are independent

Yes. Because the sample size is less than 5% of the population size, it is reasonable to treat the events as independent.

Suppose two events E and F are disjoint. What is P(E and F)?

0

Explain how to find the mean of a discrete random variable.

To find the mean of a random variable, multiply each value of the random variable by its probability and then add those products.

Twenty percent of adults in a particular community have at least a bachelor's degree. Suppose x is a binomial random variable that counts the number of adults with at least a bachelor's degree in a random sample of 100 adults from the community. Which of the following probability statements indicates the probability that fewer than 30 adults have at least a bachelor's degree?

P(x less than 30)

Identify the requirements for a discrete probability distribution.

The sum of the probabilities must equal one. Each probability must be between zero and one inclusive.

What does it mean to say that the trials in a binomial experiment are independent of each other?

The outcome of one trial does not affect the outcomes of the other trials.

What is the mean of a probability distribution?

The mean is the expected value of the random variable

How many trials are in the experiment?

25

Which of the following statements is not true about binomial probability distributions?

As the probability of success increases, the probability distribution for a binomial variable becomes bell shaped.

Suppose you are trying to calculate the probability that someone passes statistics on the first attempt given that they received an A in their previous math course. Which probability do you divide by when using conditional probability rule?

the probability that someone received an A in their previous math course

When a constant is added (or subtracted) to each value of a random variable, which measures do not increase (or decrease) by that same amount?

measures of spread

The probability that a randomly selected adult in a particular community is a smoker is 20%. The probability that a randomly selected adult in the community is a smoker, given that the adult earns more than $75,000 per year, is 10%. Are the events "is a smoker" and "earns more than $75,000 peryear" independent? Explain.

No, because the probability of smoking is different for people who earn over $75,000 peryear, the events are not independent.

How would you find the probability that a man in this age category does NOT die of cancer during the course of the year?

1-0.003

Which of the following is not a valid explanation of the Law of Large Numbers

These statements are all valid

If two events E and F are independent, then P(E and F)=

P(E) x P(F)

is used for the probability of failure on any trial in a binomial experiment.

1-p

If two events E and F are not independent, then P(E and F)equals=

P(E) x P(F/E)

Cards are drawn with replacement from a standard deck until a king is drawn. Does this constitute a binomial experiment

No, because there is not a fixed number of trials.

When considering events resulting from a single trial, if one event is the complement of anotherevent, must those two events be disjoint

Yes; There is no overlap between an event occurring and the event not occurring. They are completely separate and disjoint.

Suppose you want to know how likely it is that a student graduates with a Bachelor's degree in 4 years if they were in the top 10% of their high school graduating class. Which of the following probabilities will answer your question

P(earn BS degree|top 10%)

is used for the probability of sucess on any trial in a binomial experiment

p

Explain how to read the notation P(E|F).

the probability of E given F

Which terms are used to describe events that have no outcomes in common

disjoint or mutually exclusive

The binomial probability distribution is a __________ probability distribution that describes probabilities for experiments in which there are two __________ outcomes.

discrete

mutually ecxlusive

Use symbols to describe the event that a college student is female given that he/she has financial aid.

A|B

random variable has infinitely many values which can be plotted on a number line in an uninterrupted fashion.

continuous

Describe the event C|A in words.

A college student finishes his/her undergraduate degree in four years given that the student is female.

Suppose that a binomial random variable X is counting the number of patients with cancer at a particular hospital. How will "success" be defined in this situation?

Success would be defined as selecting a patient at the hospital who has cancer.

Describe how the value of n affects the shape of the binomial probability histogram.

As n increases, the binomial distribution becomes more bell-shaped.

How would you find the probability that no men out of 1,000 of this age will die of cancer during the course of the year?

(0.997)^1000

How would you find the probability that at least 1 man out of 1,000 of this age will die of cancer during the course of the year?

1-(0.997)^1000

Which of the following is not a criterion for the binomial distribution?

The trials must be dependent.

Twenty percent of adults in a particular community have at least a bachelor's degree. Suppose x is a binomial random variable that counts the number of adults with at least a bachelor's degree in a random sample of 100 adults from the community. If you are using the binomial probability formula, which of the following is the most efficient way to calculate the probability that at most 98 adults have a bachelor's degree, P(xless than or equals≤98)?

1−P(x=99)−P(x=100)

Use symbols to describe the event that a college student finishes his/her undergraduate degree in four years if she/he does not have financial aid

C|B'