Deck 4: Probability and Probability Distributions

Question 1

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

Answer 1

A

Question 2

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

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

Answer 2

A

Question 3

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

Answer 3

A

Question 4

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

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

Question 5

If two events are collectively exhaustive,what is the probability that one or the other occurs?

A)0.25
B)0.50
C)1.00
D)Cannot be determined from the information given.

Question 6

Let A and B be the events of the FDA approving and rejecting a new drug to treat hypertension,respectively.The events A and B are:

A)independent
B)conditional
C)unilateral
D)mutually exclusive

Question 7

The law of large numbers is relevant to the estimation of

A)objective probabilities
B)subjective probabilities
C)both of these options
D)neither of these options

Question 8

The joint probabilities shown in a table with two rows, and and two columns, and ,are as follows: P( and )= .10,P( and )= .30,P( and )= .05,and P( and )= .55.Then P( | ),calculated up to two decimals,is

A).33
B).35
C).65
D).67

Question 9

If two events are mutually exclusive and collectively exhaustive,what is the probability that both occur?

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

Question 10

A discrete probability distribution:

A)lists all of the possible values of the random variable and their corresponding probabilities
B)is a 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 11

Which of the following statements are true?

A)Probabilities must be nonnegative
B)Probabilities must be less than or equal to 1
C)The sum of all probabilities for a random variable must be equal to 1
D)All of these options are true.

Question 12

is the:

A)addition rule
B)commutative rule
C)rule of complements
D)rule of opposites

Question 13

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)Cannot be determined from the information given.

Question 14

Probabilities that can be estimated from long-run relative frequencies of events are

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

Question 15

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

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

Question 16

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 17

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

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

Question 18

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

A)mutually exclusive
B)independent
C)exhaustive
D)complementary

Question 19

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)Cannot be determined with the information given

Question 20

If two events are mutually exclusive,what is the probability that one or the other occurs?

A)0.25
B)0.50
C)1.00
D)Cannot be determined from the information given.

Question 21

Which of the following best describes the concept of marginal probability?

A)It is a measure of the likelihood that a particular event will occur,regardless of whether another event occurs.
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 the above.

Question 22

If A and B are any two events with P(A)= .8 and P(B| )= .7,then P( and B)is

A).56
B).14
C).24
D)None of the above

Question 23

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

Question 24

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

A)0
B)0.50
C)1.00
D)Cannot be determined from the information given

Question 25

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

Question 26

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

Question 27

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

Question 28

If A and B are mutually exclusive events with P(A)= 0.30 and P(B)= 0.40,then the probability that either A or B or both occur is:

A)0.10
B)0.12
C)0.70
D)None of the above

Question 29

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 30

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

Question 31

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

Question 32

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

Question 33

The joint probabilities shown in a table with two rows, and and two columns, and ,are as follows: P( and )= .10,P( and )= .30,P( and )= .05,and P( and )= .55.Then P( | ),calculated up to two decimals,is

A).33
B).35
C).65
D).67

Question 34

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

Question 35

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

Question 36

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

Question 37

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)Cannot be determined from the information given

Question 38

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

Question 39

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

Question 40

If A and B are any two events with P(A)= .8 and P(B|A)= .4,then the joint probability of A and B is

A).80
B).40
C).32
D)1.20

Question 41

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

Question 42

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

Question 43

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

Question 44

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 45

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

Question 46

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

Question 47

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 48

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.

Question 49

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

Question 50

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 51

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

Question 52

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 53

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

Question 54

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

Question 55

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 56

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

Question 57

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

Question 58

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

Question 59

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 60

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

Question 61

What is the probability that this project will not be completed on time?

Question 62

What is the probability that the price of this product will be above its mean in the upcoming quarter?

Question 63

Determine the marginal probability distribution of .

Question 64

What is the probability that no one is waiting or being served in the regular checkout line?

Question 65

Find the marginal distribution of Y.What does this distribution tell you?

Question 66

On average,how many customers would you expect to see in each of these two lines at the grocery store?

Question 67

What is the probability that the demand of this product exceed 2500 units in the upcoming quarter,given that its price will be less than $30?

Question 68

What is the probability that the demand of this product will be below its mean in the upcoming quarter?

Question 69

Find the marginal distribution of X.What does this distribution tell you?

Question 70

What is the probability that no one is waiting or being served in the express checkout line?

Question 71

What is the probability that this project will be completed in less than 4 months from now?

Question 72

(A)Calculate the conditional distribution of X given Y.
(B)What is the practical benefit of knowing the conditional distribution in (A)?

Question 73

What is the probability that no more than two customers are waiting in both lines combined?

Question 74

Calculate the conditional distribution of Y given X.

Question 75

Find the probability distribution of X.

Question 76

Find the expected price and demand level for the upcoming quarter.

Question 77

Calculate the joint probabilities of and .

Question 78

What is the probability that the demand of this product will be less than 3500 units in the upcoming quarter,given that its price will be greater than $20?

Question 79

Are and independent random variables? Explain why or why not.

Question 80

(A)What is the expected completion time (in months)from now for this project?
(B)How much variability (in months)exists around the expected value found in (A)?