Deck 5: Probability and Probability Distributions

Question 1

Given that events A and B are independent and that P(A)= 0.8 and P(B/A)= 0.4,then P(A and B)= 0.32.

Answer 1

True

Question 2

Two or more events are said to be exhaustive if one of them must occur.

Answer 2

True

Question 3

If P(A and B)= 1,then A and B must be collectively exhaustive.

Answer 3

True

Question 4

If P(A and B)= 0,then A and B must be collectively exhaustive.

Question 5

Two events are said to be independent when knowledge of one event is of no value when assessing the probability of the other.

Question 6

The relative frequency of an event is the number of times the event occurs out of the total number of times the random experiment is run.

Question 7

Suppose that after graduation,you will either buy a new car (event A)or take a trip to Europe (event B).In this case,events A and B are mutually exclusive.

Question 8

Two or more events are said to be exhaustive if at most one of them can occur.

Question 9

Conditional probability is the probability that an event will occur,with no other events taken into consideration.

Question 10

You think you have a 90% chance of passing your statistics class.This is an example of subjective probability.

Question 11

Probability is a number between 0 and 1,inclusive,which measures the likelihood that some event will occur.

Question 12

Two or more events are said to be mutually exclusive if at most one of them can occur.

Question 13

If A and B are independent events with P(A)= 0.40 and P(B)= 0.50,then P(A/B)is 0.50.

Question 14

Two events A and B are said to mutually be exclusive if P(A and B)= 0.

Question 15

The law of large numbers states that subjective probabilities can be estimated based on the long run relative frequencies of events.

Question 16

If A and B are two independent events with P(A)= 0.20 and P(B)= 0.60,then P(A and B)= 0.80.

Question 17

Suppose A and B are mutually exclusive events where P(A)= 0.3 and P(B)= 0.4.Then,P(A and B)= 0.12.

Question 18

The multiplication rule for two events A and B is: P(A and B)= P(A|B)P(A).

Question 19

If events A and B have nonzero probabilities,then they can be both independent and mutually exclusive.

Question 20

Suppose A and B are two events where P(A)= 0.5,P(B)= 0.4,and P(A and B)= 0.2,then P(B/A)= 0.5.

Question 21

A random variable X is standardized when each value of X has the mean of X subtracted from it,and the difference is divided by the standard deviation of X.

Question 22

If the random variable X is normally distributed with mean and standard deviation ,then the random variable Z defined by is also normally distributed with mean 0 and standard deviation 1.

Question 23

Using the standard normal distribution,the Z-score representing the 5th percentile is 1.645.

Question 24

The mean and standard deviation of a normally distributed random variable that has been "standardized" are zero and one,respectively.

Question 25

​A probability tree is a graphical representation of how events occur through time,which is useful for calculating probabilities.

Question 26

Subjective probability is the probability that a given event will occur,given that another event has already occurred.

Question 27

Football teams toss a coin to see who will get their choice of kicking or receiving to begin a game.The probability that given team will win the toss three games in a row is 0.125.

Question 28

Two events A and B are said to be independent if P(A and B)= P(A)+ P(B).

Question 29

Suppose A and B are mutually exclusive events where P(A)= 0.2 and P(B)= 0.5,then P(A or B)= 0.70.

Question 30

When we wish to determine the probability that at least one of several events will occur,we would use the addition rule.

Question 31

The number of car insurance policy holders is an example of a discrete random variable.

Question 32

Using the standard normal distribution,the Z- score representing the 99th percentile is 2.326.

Question 33

The number of people entering a shopping mall on a given day is an example of a discrete random variable.

Question 34

The time students spend in a computer lab during one day is an example of a continuous random variable.

Question 35

When two events are independent,they are also mutually exclusive.

Question 36

The number of cars produced by GM during a given quarter is a continuous random variable.

Question 37

The total area under the normal distribution curve is equal to one.

Question 38

The temperature of the room in which you are writing this test is a continuous random variable.

Question 39

The probability that event A will not occur is denoted as .

Question 40

A random variable is a function that associates a numerical value with each possible outcome of a random phenomenon.

Question 41

The variance of a binomial distribution is given by the formula ,where n is the number of trials,and p is the probability of success in any trial.

Question 42

The Poisson random variable is a discrete random variable with infinitely many possible values.

Question 43

The number of loan defaults per month at a bank is Poisson distributed.

Question 44

Using the standard normal curve,the Z- score representing the 75th percentile is 0.674.

Question 45

An exponential distribution with parameter = 0.2 has mean and standard deviation both equal to 5.

Question 46

The Poisson distribution is characterized by a single parameter ,which must be positive.

Question 47

A binomial distribution with n number of trials,and probability of success p can be approximated well by a normal distribution with mean np and variance if np > 5 and n(1-p)> 5.

Question 48

The binomial distribution is a discrete distribution that deals with a sequence of identical trials,each of which have only two possible outcomes.

Question 49

The variance of a binomial distribution for which n = 50 and p = 0.20 is 8.0.

Question 50

Using the standard normal curve,the Z- score representing the 10th percentile is 1.28.

Question 51

A Poisson distribution is appropriate to determine the probability of a given number of defective items in a shipment.

Question 52

Much of the study of probabilistic inventory models,queuing models,and reliability models relies heavily on the Poisson and exponential distributions.

Question 53

The binomial random variable represents the number of successes that occur in a specific period of time.

Question 54

A random variable X is normally distributed with a mean of 175 and a standard deviation of 50.Given that X = 150,its corresponding Z- score is -0.50.

Question 55

The Poisson probability distribution is one of the most commonly used continuous probability distributions.

Question 56

For a given probability of success p that is not too close to 0 or 1,the binomial distribution takes on more of a symmetric bell shape as the number of trials n increases.

Question 57

The density function specifies the probability distribution of a continuous random variable.​

Question 58

The binomial distribution deals with consecutive trials,each of which has two possible outcomes.

Question 59

The Poisson distribution is applied to events for which the probability of occurrence over a given span of time,space,or distance is very small.

Question 60

The binomial distribution is a continuous distribution.

Question 61

A function that associates a numerical value with each possible outcome of an uncertain event is called a _____ variable.

A)conditional
B)random
C)population
D)sample

Question 62

The probabilities shown in a table with two rows, and and two columns, and ,are as follows: P( and )= 0.10,P( and )= 0.30,P( and )= 0.05,and P( and )= 0.55.Then P( | )is

A)0.33.
B)0.35.
C)0.65.
D)0.67.

Question 63

Probabilities that can be estimated from long-run relative frequencies of events are called _____ probabilities.

A)objective
B)subjective
C)complementary
D)joint

Question 64

The probability of an event and the probability of its complement always sum to

A)1.
B)0.
C)any value between 0 and 1.
D)any positive value.

Question 65

If A and B are mutually exclusive events with P(A)= 0.70,then P(B)

A)can be any value between 0 and 1.
B)can be any value between 0 and 0.70.
C)cannot be larger than 0.30.
D)can be any value between 0.30 and 0.70.

Question 66

Which of the following statements is true?

A)Probabilities must be negative.
B)Probabilities must be greater than 1.
C)The sum of all probabilities for a random variable must be equal to 1.
D)The sum of all probabilities for a random variable must be equal to 0.

Question 67

If two events are independent,what is the probability that they both occur?

A)0
B)0.50
C)1.00
D)This cannot be determined from the information given.

Question 68

A discrete probability distribution

A)is a set of possible values and a corresponding set of probabilities that sum to 1.
B)is a modeling tool that can be used to incorporate uncertainty into models.
C)can be estimated from long-run proportions.
D)is the distribution of a single random variable.

Question 69

If events A and B are mutually exclusive,then the probability of both events occurring simultaneously is equal to

A)0.0.
B)0.5.
C)1.0.
D)any value between 0.5 and 1.0.

Question 70

There are two types of random variables,they are

A)discrete and continuous.
B)exhaustive and mutually exclusive.
C)complementary and cumulative.
D)real and unreal.

Question 71

If P(A)= P(A|B),then events A and B are said to be

A)mutually exclusive.
B)independent.
C)dependent.
D)complementary.

Question 72

The probabilities shown in a table with two rows, and and two columns, and ,are as follows: P( and )= 0.10,P( and )= 0.30,P( and )= 0.05,and P( and )= 0.55.Then P( | ),calculated up to two decimals,is

A)0.33.
B)0.35.
C)0.65.
D)0.67.

Question 73

If P(A)= 0.25 and P(B)= 0.65,then P(A and B)is

A)0.25.
B)0.40.
C)0.90.
D)This cannot be determined from the information given.

Question 74

If two events are collectively exhaustive,what is the probability that both occur at the same time?

A)0.00
B)0.50
C)1.00
D)This cannot be determined from the information given.

Question 75

The formal way to revise probabilities based on new information is to use _____ probabilities.

A)complementary
B)conditional
C)unilateral
D)common sense

Question 76

Probabilities that cannot be estimated from long-run relative frequencies of events are called

A)objective probabilities.
B)subjective probabilities.
C)complementary probabilities.
D)joint probabilities.

Question 77

If two events are mutually exclusive,what is the probability that both occur at the same time?

A)0.0
B)0.5
C)1.0
D)This can be any probability between 0 and 1.

Question 78

The law of large numbers is relevant to the estimation of _____ probabilities.

A)objective
B)subjective
C)both objective and subjective
D)neither objective nor subjective

Question 79

If A and B are any two events with P(A)= 0.8 and P(B|A)= 0.4,then the joint probability of A and B is:

A)0.80
B)0.40
C)0.32
D)1.20

Question 80

Which of the following best describes the concept of probability?

A)It is a measure of the likelihood that a particular event will occur.
B)It is a measure of the likelihood that a particular event will occur,given that another event has already occurred.
C)It is a measure of the likelihood of the simultaneous occurrence of two or more events.
D)None of these choices describe the concept of probability.