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Statistic and Probability II

Total questions: 81

Worksheet time: 1hrs 1mins

Name
Class
Date
1.
Mary is a good student. The probability that she studies and passes her test is 3/5. If the probability that she studies is 8/9. What is the probability that she passes given that she studies? 
a)
27/40
b)
1.48
c)
.008
d)
.0593
2.
What is the probability that a student does play a sport given they do not play an instrument? 
a)
.2
b)
.2222
c)
.10
d)
.5
3.

Consider the following table with information about all of the students taking Statistics at Happy High School.


Find P( Full-time | Male)

a)

7/3

b)

3/10

c)

3/7

d)

4/7

4.

Consider the following table with information about all of the students taking Statistics at Happy High School.


Find P( Female | Part-time) =

a)

15/31

b)

43/71

c)

31/43

d)

15/43

5.

A new credit card has been issued to 2000 customers. Of these customers, 1500 hold a Visa, 500 hold an AA card, and 40 hold a Visa and AA card. Find the probability that a random chosen customer holds an AA, given they hold a Visa.

a)

.0267

b)

37.5

c)

.02

d)

.3333

6.
P(Sandals|Pants):
a)
4/20
b)
6/15
c)
1/2
d)
2/7
7.
The weather forecaster predicted it will be 4/5 chance of rain for Monday and 2/3 chance of rain for Tuesday. What is the probability it will rain both days?
a)
1/2
b)
20/15
c)
8/15
d)
6/8
8.

A science teacher gave her class two tests. 25% of the class passed both tests and 42% of the class passed the first test. What percent of those who passed the first test also passed the second?

a)

59.5%

b)

10.5%

c)

1.6%

d)

Not enough information

9.

A jar contains black and white marbles. Two marbles are chosen without replacement. The probability of selecting a black marble and then a white marble is 0.34, and the probability of selecting a black marble on the first draw is 0.47. What is the probability of selecting a white marble on the second draw, given that the first marble drawn was black?

a)

16%

b)

1.38%

c)

72.3%

d)

Not enough information

10.

45% total of the children in a school have a dog, 30% total have a cat, and 18% have a dog and cat. What percent of those who have a cat also have a dog?

a)

60%

b)

40%

c)

24%

d)

1.7%

11.

Tom will randomly select from a treat bag containing 6 lollipops and 4 gum balls. Tome will select a treat, replace it, and then select a second treat.

a)

Independent

b)

Dependent

12.

Sue will randomly select from a treat bag containing 6 lollipops and 4 gum balls. Sue will select a treat, not replace it, and then select a second treat.

a)

Independent

b)

Dependent

13.

What is the probability when Tom will randomly select from a treat bag containing 6 lollipops and 4 gum balls. Tom will select a 1 lollipop, replace it, and then select a 1 gum ball.

a)

1/24

b)

1/90

c)

6/25

d)

1/10

14.

What is the probability when Sue will randomly select from a treat bag containing 6 lollipops and 4 gum balls. Sue will select a treat, not replace it, and then select a second treat. Sue will select a gum ball then a lollipop.

a)

1/24

b)

4/15

c)

1/100

d)

2/10

15.

Two fair coins are flipped at the same time. What is the probability that both with display heads?

a)

1/2

b)

1/4

c)

2%

d)

1%

16.

Two fair coins are flipped at the same time. What is the probability that both with display heads?

a)

Independent

b)

Dependent

17.

A box contains 9 new light bulbs and 6 used light bulbs. Each light bulb is the same size and shape. Meredith will randomly select 2 light bulbs from the box without replacement. What is the probability Meredith will select a new light bulb and then a used light bulb?

a)

1/54

b)

2/15

c)

6/25

d)

9/35

18.

You are at the movies with your friends and decided to buy a small bag of gummy bears. There are 4 red bears, 5 green bears, and 3 yellow bears in the bag. What is the probability that you will get yellow gummy bears and then red gummy bears?

a)

The probability is 3/11

b)

The probability is 1/11

c)

The probability is 3/132

d)

The probability is 3/12

19.

A spinner consists of two A’s, three B’s, and three C’s. What is the probability of spinning a B and then an A?

a)

2/8

b)

3/28

c)

3/32

d)

1/4

20.

A box contains 3 black pens, 7 blue pens, and 5 red pens. Without looking, P(red and black)

a)

1/14

b)

1/15

c)

2/15

d)

3/15

21.
According to Bayes' Theorem, P(A|B) =
a)
P(A and B)/[ P(A and B) + P(A' and B) ]
b)
P(A or B)/[ P(A or B) + P(A' or B) ]
c)
P(A and B)/[ P(A and B) + P(A and B') ]
d)
P(A and B)/[ P(A and B)  P(A' and B) ]⋅
22.
The estimated probabilities of an Event before any new data is collected are known as _______ probabilities
a)
Prior
b)
Posterior
c)
Conditional
d)
Simple
23.
The updated probabilities of an Event in light of newly-collected data are known as _______ probabilities
a)
Prior
b)
Posterior
c)
Conditional
d)
Simple
24.
If P(A) = 0.20, P(B|A)=0.60 and P(B|A')=0.25, then P(A|B) = 
a)
0.3750
b)
0.7059
c)
0.6250
d)
0.2941
25.
A virus has infected 1.8% of a population. A test detects this virus 95% of the time when it is actually present, but it returns a false positive 3% of the time when the virus is not present.
If a person selected at random from this population tests positive for the virus, what is the probability that this person is actually infected? [Round to the nearest percent.]
a)
37%
b)
63%
c)
34%
d)
66%
26.
A witness claims that a black car was involved in a nighttime accident. Police know that, at night, witnesses identify black cars correctly 90% of the time, but 30% of the time misidentify cars of other colors as black.
If 8% of cars in the city are black, what is the probability that a black car really was involved in the accident?
a)
0.2069
b)
0.0845
c)
0.7931
d)
0.6200
27.
A rare species of dragonfly is always born with an extra set of wings. However, common dragonflies also sometimes get an extra set of wings through a mutation. 0.3% of dragonflies in a certain habitat belong to this rare species, and the extra-wing mutation is known to occur in 0.1% of common dragonflies.
You see a dragonfly in this habitat with an extra pair of wings. What is the probability that it is a member of the rare species?
a)
0.7506
b)
0.1003
c)
0.0004
d)
0.9996
28.
Suppose that 5% of companies in a certain industry discriminate against Iowans. If a company discriminates, it will never hire someone from Iowa.
Suppose that 20 equally-qualified applicants apply for jobs at a company in this industry, and six are from Iowa. If this company hires four people from this set of applicants, but none are from Iowa, what is the probability that this company discriminates?
a)
0.2030
b)
0.7970
c)
0.5095
d)
0.4905
29.
83% of a certain airline's flights depart on time. Of these flights, 90% also arrive on time. 30% of flights from this airline that depart late manage to make up time in the air to still arrive on time.
You see a flight from this airline arriving on time. What is the probability that it departed on time?
a)
0.9361
b)
0.9608
c)
0.9721
d)
0.8532
30.
Urn A contains three white and five black balls. Urn B contains two white and eight black balls.
I hand you one of these urns at random and you select a ball from that urn at random.
If that ball is white, what is the probability that I handed you Urn A? [Round to the nearest percent.]
a)
60%
b)
65%
c)
55%
d)
70%
31.
The updated probabilities of an Event in light of newly-collected data are known as _______ probabilities
a)
Prior
b)
Posterior
c)
Conditional
d)
Simple
32.
The estimated probabilities of an Event before any new data is collected are known as _______ probabilities
a)
Prior
b)
Posterior
c)
Conditional
d)
Simple
33.
If P(A) = 0.20, P(B|A)=0.60 and P(B|A')=0.25, then P(A|B) = 
a)
0.3750
b)
0.7059
c)
0.6250
d)
0.2941
34.
A virus has infected 1.8% of a population. A test detects this virus 95% of the time when it is actually present, but it returns a false positive 3% of the time when the virus is not present.
If a person selected at random from this population tests positive for the virus, what is the probability that this person is actually infected? [Round to the nearest percent.]
a)
37%
b)
63%
c)
34%
d)
66%
35.

What is the formula for conditional probability?

a)

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

b)

P(A|B) = P(A) - P(B)

c)

P(A|B) = P(A) * P(B)

d)

P(A|B) = P(A ∩ B) / P(B)

36.

In a deck of 52 cards, what is the probability of drawing a king given that the card drawn is a face card?

a)

1/4

b)

1/2

c)

1/3

d)

1/5

37.

Explain Bayes' theorem and provide an example of its application.

a)

Bayes' theorem is used in medical diagnosis, such as in the case of a patient testing positive for a disease and the calculation of the actual probability of having the disease given the test result and the prevalence of the disease in the population.

b)

Bayes' theorem is used in cooking recipes, such as calculating the probability of a dish turning out well based on the ingredients used

c)

Bayes' theorem is used in weather forecasting, such as predicting the chance of rain based on historical data

d)

Bayes' theorem is used in sports betting, such as determining the likelihood of a team winning based on their previous performance

38.

A bag contains 3 red balls and 2 green balls. If a ball is drawn at random, what is the probability that it is red given that it is not green?

a)

1/5

b)

3/5

c)

4/5

d)

2/5

39.

What is the difference between marginal probability and conditional probability?

a)

Marginal probability is the probability of an event occurring given that another event has already occurred, while conditional probability is the probability of an event occurring without any condition.

b)

Marginal probability is the probability of an event occurring given that another event has already occurred, while conditional probability is the probability of an event occurring given that another event has already occurred.

c)

Marginal probability is the probability of an event occurring without any condition, while conditional probability is the probability of an event occurring without any condition.

d)

Marginal probability is the probability of an event occurring without any condition, while conditional probability is the probability of an event occurring given that another event has already occurred.

40.

In a survey, 60% of people like chocolate ice cream, 40% like vanilla ice cream, and 30% like both. What is the probability that a person chosen at random likes chocolate or vanilla ice cream?

a)

20%

b)

80%

c)

50%

d)

70%

41.

If P(A) = 0.4, P(B) = 0.3, and P(A|B) = 0.5, what is P(B|A)?

a)

0.8

b)

0.2

c)

0.375

d)

0.6

42.

A factory produces 3 types of products: A, B, and C. The probability of a product being defective is 0.1, 0.15, and 0.2 for A, B, and C respectively. If a defective product is found, what is the probability that it is type B?

a)

0.05

b)

0.3

c)

0.18

d)

0.2143

43.

What is the general formula for Bayes' theorem?

a)

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

b)

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

c)

P(A|B) = (P(A) * P(B)) / (P(A) + P(B))

d)

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

44.

In a class, 60% of students are girls and 40% are boys. If 70% of the girls and 80% of the boys passed the exam, what is the probability that a student who passed the exam is a girl?

a)

0.6

b)

0.4

c)

0.7

d)

0.8

45.

A probability law used to compute the probability of the union of two events. It is P(a ∙ B) = P(a) + P(B) − P(a ∩ B). For mutually exclusive events, P(a ∩ B) = 0; in this case the addition law reduces to P(a ∙ B) = P(a) + P(B).

a)

Addition Law

b)

Bayes Theorem

c)

Classical Method

d)

Conditional Probability

46.

Two requirements that restrict the man- ner in which probability assignments can be made: (1) for each experimental outcome Ei we must have 0 ≤ P(Ei) ≤ 1; (2) considering all experimental outcomes, we must have P(E1) + P(E2) + . . . + P(En) = 1.0.

a)

Multiplication Law

b)

Combination

c)

Basic requirements for assigning probabilities

d)

Mutually Exclusive Events

47.

A method used to compute posterior probabilities.

a)

Joint Probability

b)

Bayes’ theorem

c)

marginal Probability

d)

Multiplication Law

48.

A method of assigning probabilities that is appropriate when all the experimental outcomes are equally likely.

a)

Independent Events

b)

Combination

c)

Multi-step Experiment

d)

Classical method

49.

In an experiment we may be interested in determining the number of ways n objects may be selected from among n objects without regard to the order in which the n objects are selected.

a)

Complement of A

b)

Conditional Probability

c)

Combination

d)

Intersection of A & B

50.

The event consisting of all sample points that are not in a.

a)

Complement of A

b)

Event

c)

Independent Events

d)

Intersection of A & B

51.

The probability of an event given that another event already occurred. The conditional probability of a given B is P(a ∣ B) = P(a ∩ B)/P(B

a)

Conditional probability

b)

Marginal probability

c)

Joint probability

d)

Multiplication law

52.

A collection of sample points.

a)

Experiment

b)

Independent events

c)

Event

d)

Mutually exclusive events

53.

A process that generates well-defined outcomes.

a)

Combination

b)

Complement of A

c)

Event

d)

Experiment

54.

Two events a and B where P(a ∣ B) = P(a) or P(B ∣ a) = P(B); that is, the events have no influence on each other.

a)

Multiple-step experiment

b)

Independent events

c)

Event

d)

Experiment

55.

The event containing the sample points belonging to both a and B. The intersection is denoted a ∩ B.

a)

Event

b)

Joint probability

c)

intersection of A and B

d)

Experiment

56.

The probability of two events both occurring; that is, the probability of the intersection of two events.

a)

Conditional probability

b)

Multiplication law

c)

Marginal probability

d)

Joint Probability

57.

The values in the margins of a joint probability table that provide the probabilities of each event separately.

a)

Marginal Probability

b)

Joint Probability

c)

Conditional Probability

d)

Classical Method

58.

An experiment that can be described as a sequence of steps.

a)

Experiment

b)

Event

c)

Multi-step Experiment

d)

Marginal Probability

59.

A probability law used to compute the probability of the intersection of two events. It is P(a ∩ B) = P(B)P(a ∣ B) or P(a ∩ B) = P(a)P(B ∣ a). For independent events it reduces to P(a ∩ B) = P(a)P(B).

a)

Baye's Theorem

b)

Multiplication Law

c)

Joint Probability

d)

Marginal Probability

60.

Events that have no sample points in common; that is, a ∩ B is empty and P(a ∩ B) = 0.

a)

Mutually exclusive events

b)

Independent events

c)

Event

d)

Experiment

61.

In an experiment we may be interested in determining the number of ways n objects may be selected from among n objects when the order in which the n objects are selected is important.

a)

Probability

b)

Sample Point

c)

Permutation

d)

Prior Probabilities

62.

Revised probabilities of events based on additional information.

a)

Subjective method

b)

Prior probabilities

c)

Probability

d)

Posterior probabilities

63.

Initial estimates of the probabilities of events.

a)

Posterior probabilities

b)

Probability

c)

Prior probabilities

d)

Relative frequency method

64.

A numerical measure of the likelihood that an event will occur.

a)
probability
b)
possibility
c)
chance
d)
certainty
65.

A method of assigning probabilities that is appropriate when data are available to estimate the proportion of the time the experimental outcome will occur if the experiment is repeated a large number of times.

a)
conditional probability
b)

Relative Frequency Method

c)
empirical probability
d)
subjective probability
66.

An element of the sample space. A sample point represents an experimental outcome.

a)
Event point
b)
Sample point
c)
Experiment point
d)
Outcome point
67.

The set of all experimental outcomes

a)
outcome set
b)
sample space
c)
result space
d)
experimental set
68.

A method of assigning probabilities on the basis of judgment.

a)

unreliable method

b)

objective method

c)

random method

d)

subjective method

69.

A graphical representation that helps in visualizing a multiple-step experiment

a)
pie chart
b)

tree diagram

c)
bar graph
d)
line plot
70.

The event containing all sample points belonging to a or B or both. The union is denoted a ∙ B.

a)

Union of A & B

b)

Event

c)

Experiment

d)

Joint Probability

71.

A graphical representation for showing symbolically the sample space and operations involving events in which the sample space is represented by a rectangle and events are represented as circles within the sample space.

a)
Venn diagram
b)
Bar chart
c)
Line graph
d)
Pie chart
72.

A composite price index based on the prices of a group of items.

a)
Composite Price Index
b)
Group Price Index
c)
Combined Price Index
d)
Aggregate Price Index
73.

A monthly price index that uses the price changes in a market basket of consumer goods and services to measure the changes in consumer prices over time.

a)
Market Price Index (MPI)
b)
Consumer Price Index (CPI)
c)
Retail Price Index (RPI)
d)
Gross Domestic Product (GDP)
74.

Aggregate price indexes designed to show price trends and movements associated with common stocks

a)
stock value indexes
b)
stock exchange indexes
c)

Dow Jones averages

d)
stock market indexes
75.

A quantity index designed to measure changes in the physi- cal volume or production levels of industrial goods over time.

a)
Industrial Production Index
b)
Industrial Volume Indicator
c)
Manufacturing Output Index
d)
Production Quantity Index
76.

A weighted aggregate price index in which the weight for each item is its base-period quantity.

a)
Marshall-Edgeworth index
b)
Laspeyres index
c)
Fisher index
d)
Paasche index
77.

A weighted aggregate price index in which the weight for each item is its current-period quantity

a)
Paasche index
b)
Fisher index
c)
Marshall-Edgeworth index
d)

Paasche index

78.

A price index for a given item that is computed by dividing a current unit price by a base-period unit price and multiplying the result by 100

a)
Price Comparison
b)
Price Relative
c)
Price Index
d)
Price Ratio
79.

A monthly price index designed to measure changes in prices of goods sold in primary markets (i.e., first purchase of a commodity in nonretail markets).

a)
Consumer Price Index (CPI)
b)
Retail Price Index (RPI)
c)
Wholesale Price Index (WPI)
d)
Producer Price Index (PPI)
80.

An index designed to measure changes in quantities over time

a)
Gross Domestic Product (GDP)
b)
Interest Rate
c)

Quantity Index

d)
Unemployment Rate
81.

A composite price index in which the prices of the items in the composite are weighted by their relative importance.

a)
composite price index
b)
relative price index
c)
weighted index
d)

weighted aggregate price index

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