Deck 4: Probability and Probability Distributions

Question 1

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

Answer 1

True

Question 2

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

Answer 2

False

Question 3

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

Answer 3

True

Question 4

The probability that event A will not occur is denoted as $P ( \bar { A } )$ .

Question 5

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

Question 6

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 7

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

Question 8

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 9

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

Question 10

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

Question 11

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 12

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

Question 13

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 14

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

Question 15

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

Question 16

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

Question 17

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

Question 18

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

Question 19

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 20

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

Question 21

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 22

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 23

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

Question 24

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

Question 25

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 26

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 27

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 28

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

Question 29

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

Question 30

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

Question 31

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

Question 32

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 33

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 occur is:

A) 0.10
B) 0.12
C) 0.70
D) None of these options.

Question 34

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 35

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 36

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 37

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

Question 38

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

Question 39

Which of the following statements are 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) All of these options are true.

Question 40

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

Question 41

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
Suppose that patrons of a restaurant were asked whether they preferred beer or whether they preferred wine.60% said that they preferred beer.70% of the patrons were male.80% of the males preferred beer.

Question 42

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 43

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 44

The probabilities shown in a table with two rows, $A _ { 1 } \text { and } A _ { 2 }$
And two columns, $B _ { 1 } \text { and } B _ { 2 }$
,are as follows: $P \left( A _ { 1 } \text { and } B _ { 1 } \right) = .10$
, $P \left( A _ { 1 } \text { and } B _ { 2 } \right) = .30$
, $P \left( A _ { 2 } \text { and } B _ { 1 } \right) = .05$
,and $P \left( A _ { 2 } \text { and } B _ { 2 } \right) = .55$
)Then $P \left( A _ { 1 } \mid B _ { 2 } \right)$
,calculated up to two decimals,is

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

Question 45

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 46

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 47

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 options.

Question 48

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.

Question 49

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 50

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 51

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 52

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 53

The law of large numbers is relevant to the estimation of

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

Question 54

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 55

The probabilities shown in a table with two rows, $A _ { 1 } \text { and } A _ { 2 }$
And two columns, $B _ { 1 } \text { and } B _ { 2 }$
,are as follows: $P \left( A _ { 1 } \text { and } B _ { 1 } \right) = 10$
, $P \left( A _ { 1 } \text { and } B _ { 2 } \right) = .30$
, $P \left( A _ { 2 } \text { and } B _ { 1 } \right) = .05$
,and $P \left( A _ { 2 } \text { and } B _ { 2 } \right) = .55$
)Then $P \left( A _ { 1 } \mid B _ { 1 } \right)$
,calculated up to two decimals,is

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

Question 56

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.