QNT/275T - Wk 3 - Basic Probability and Random Variables

let A and B be independent events. the probability that A and B will both occur is _____.

P(A n B) = P(A) x P(B)

the _____ of an event is the opposite of an event. it is the set of all outcomes of an experiment that are not included in an event.

complement

The probability of event A, given that event B occurred, is known as the ___ probability of A, given B.

conditional

which rule is defined as P(A | B ) = P(A n B ) / P(B) ?

conditional probability rule

A(n) _____ is a set of sample space outcomes.

event

A(n) ______________ is a collection of sample space outcomes.

event

If the random variable x is normally distributed, 68.26 percent of all possible observed values of x will be within two standard deviations of the mean.

false

If the probability of an event is not influenced by another event occurring, then the two events are _____.

independent

Which of the following is not a discrete random variable?

the number of minutes required to run 1 mile

what is the difference between (a) the addition rule and (b) the addition rule for two mutually exclusive events?

(a) requires you to subtract the probability of intersection, (b) does not

A fair die is rolled 10 times. What is the average number of even number outcomes?

5 Binomial mean = μ = np = 10(.5) = 5

In which of the following situations would you use the counting rule for combinations?

-when you want to select two vendors to supply an office -when you want to know how many different groups of 3 people can be selected from a list of 10 people

The Post Office has established a record in a major midwestern city for delivering 90 percent of its local mail the next working day. If you mail eight local letters, what is the probability that all of them will be delivered the next day?

.4305 P(x = 8) = .4305

The mean of a standard normal distribution is always equal to

0 (zero)

It is very common for television series to draw a large audience for special events or for cliff-hanging story lines. Suppose that on one of these occasions, the special show drew viewers from 38.2 percent of all US TV households. Suppose that three TV households are randomly selected. What is the probability that all three households viewed this special show?

0.056 (.382)(.382)(.382) = .05574

the probability of an employee getting a promotion is 0.20 the probability of an employee having an MBA is 0.30 the probability of an employee getting a promotion, given that the employee has a MBA, is 0.25. what is the probability that an employee has an MBA and gets a promotion?

0.075 P(MBA n promotion) = P(MBA) x P(promotion | MBA) = 0.30 x 0.25 = 0.075

Suppose that you believe that the probability you will get a grade of B or better in Introduction to Finance is .6 and the probability that you will get a grade of B or better in Introduction to Accounting is .5. If these events are independent, what is the probability that you will receive a grade of B or better in both courses?

0.300 (.6)(.5) = .30

the probability that a customer orders popcorn is 0.40 the probability that a customer orders a drink is 0.65 the probability that a customer orders popcorn and a drink is 0.30 if a customer has already ordered a drink, what is the probability that the customer will order a popcorn?

0.46 P(popcorn | drink) = 0.30/0.65 = 0.46 P(popcorn n drink)/P(drink)

What is the probability that an even number appears on the toss of a die

0.5 Set up sample spaces: 6 total; 2, 4, and 6 are even numbers.

the probability assigned to an experimental outcome must be between zero and _____.

1

Using the following probability distribution table of the random variable x, what is the probability of x = 3?

5/15 All values of P(X) need to sum to 1, so 5/15 + 4/15 + 1/15 = 10/15 means P(X = 3) = 5/15.

A letter is drawn from the alphabet of 26 letters. What is the probability that the letter drawn is a vowel?

5/26

the conditional probability of A, given B, is calculated by dividing the probability of the intersection of A and B by the probability of _____.

B P(A | B) = P(A n B) / P(B)

when new information is used to revise a prior probability to a posterior probability, which of the following methodologies is used?

Bayes' Theorem

consider an event A and its complement a. what is P(A) + P(a)?

Either event A or its complement a must occur, therefore the sum of their probabilities is 1.

The mean of a standard normal distribution is always equal to 1.

False Mean of a standard normal distribution is 0.

Consider a standard deck of 52 playing cards, a randomly selected card from the deck, and the following events: R = red, B = black, A = ace, N = nine, D = diamond, and C = club. Are R and A mutually exclusive?

No, not mutually exclusive.

if event A and B are mutually exclusive, then _____.

P(A n B) = 0 if two events are mutually exclusive then their intersection is 0

Which of the following is an example of a conditional probability?

The probability that a student plays video games given that the student is female

Which of the following statements about the binomial distribution is not correct?

The random variable of interest is continuous.

An event is a collection of sample space outcomes

True

The standard deviation of a discrete random variable measures the spread of the population of all possible values of x.

True

the probability that a customer orders popcorn is 0.40 the probability that a customer orders a drink is 0.65 the probability that a customer orders popcorn and a drink is 0.30 if a customer has already ordered popcorn, what is the probability that the customer will order a drink?

0.75

A plant manager knows that the number of boxes of supplies received weekly is normally distributed with a mean of 200 and a standard deviation of 20. What percentage of the time will the number of boxes received in a week exceed 200?

50% P(x > 200) = p(z > 0) = .5

New car owners were asked to evaluate their experiences in buying a new car during the past 12 months. In the survey, the owners indicated they were most satisfied with their experiences at the following three dealers (in no particular order): Subaru, Honda, and Buick. When ranking the dealers, how many outcomes are possible?

6 HSB, BHS, SHB, HBS, BSH, SBH

let A and B be mutually exclusive events. the simplest way of writing the probability that A or B will occur is _____.

P(A u B) = P(A) + P(B) looking for the probability of the union of A and B --> P(A u B)

The standard deviation of a standard normal distribution is always equal to 1.

True

Which of the following symbols denotes the complement of an event A?

__ A

if the probability of an event is not influenced by another event occurring, then the two events are _____

independent

The probabilities of all the experimental outcomes of an experiment must sum to _____.

one.

an experiment is performed many times. the probabilities of the experimental outcomes are estimated to be the proportion of the time that the outcomes occurred during the many repetitions of the experiment. these are called _____ probabilities.

relative frequency relative frequency probabilities are based on repeat performances of the experiment

the probabilities of experimental outcomes are estimated by using previous experience with the similar situations, intuition, or special expertise. these are called _____ probabilities

subjective

A softball coach believes that Laurie has a 0.5 probability of getting a hit against a particular pitcher that Laurie has never batted against before. This is called a(n) _____ probability

subjective subjective probabilities are based on experience, intuitive judgment, or expertise.

which method of computing probabilities states that: the probability of an event occurring = number of sample space outcomes that correspond to the event / total number of sample space outcomes

the classical method

if an experiment consist of a three step process, what do the number of branches shown at stage three tell us?

the number of outcomes in the sample space the probabilities are not necessarily determined by the number of branches

the additional rule is used to calculate _____

the probability of the union of two events

If two events are independent, then the probability that both events occur equals _____.

the product of the individual probabilities the multiplication rule states that P(A n B) = P(A) x P(B)

A random variable is a numerical value that is determined by the outcome of an experiment.

true

A continuous probability distribution having a rectangular shape, where the probability is evenly distributed over an interval of numbers is a(n) ____________ distribution

uniform

When can the classical method of computing probabilities be used?

when all of the sample space outcomes are equally likely

in which of the following examples is the n1n2 rule appropriate?

when we want to count the number of sequences of numbers we can roll in four rolls of a die. when there are 3 possible outcomes at the first step and they can be combined with any of 4 possible outcomes at the second step.

an event that never occurs has probability equal to _____.

zero

A standard normal distribution has a mean of _____ and standard deviation of _____

zero, one

looking at the following diagram, what is the sample space

{BB, BG, GB, GG} the sample space is the set of all experimental outcomes