Question 1

A table of joint probabilities is shown below. $$\begin{array} { | c | c | c | c | } 
\hline & A _ { 1 } & A _ { 2 } & A _ { 3 } \
\hline B _ { 1 } & 0.15 & 0.25 & 0.20 \
\hline B _ { 2 } & 0.10 & 0.15 & 0.15 \
\hline
\end{array}$$ Calculate P( $B _ { 2 }$ / $A _ { 1 }$ ).

Accepted Answer

P( @#LAT-DLM& | @#LAT-DLM& ) =

Question 2

An ice cream vendor sells three flavours: chocolate, strawberry and vanilla. 45% of the sales are chocolate, 30% are strawberry and the rest are vanilla. Sales are by the cone or the cup. The percentages of cones sales for chocolate, strawberry and vanilla are 75%, 60% and 40%, respectively. For a randomly selected sale, define the following events:
AS1U1B11S1U1B0 = chocolate chosen.
AS1U1B12S1U1B0 = strawberry chosen.
AS1U1B13S1U1B0 = vanilla chosen.
B = ice cream in a cone. $\bar { B }$ = ice cream in a cup.
Use this information to answer the following question(s).
-Find the probability that the ice cream was sold in a cup and the flavour was:
a. chocolate.
b. strawberry.
c. vanilla.

Accepted Answer

a. P( @#LAT-DLM& @#LAT-DLM& @#LAT-DLM& ) = P( @#LAT-DLM& | @#LAT-DLM& ) * P( @#LAT-DLM& )

Question 3

If P(A) = 0.25 and P(B) = 0.65, then P(A$\cap$B) is:

Accepted Answer

A)  $0.25$. 
B)  $0.40$. 
C)  $0.90$. 
D)  $P ( A \curvearrowleft B )$ cannot be determined from the information given. 
A)  $0.25$. 
B)  $0.40$. 
C)  $0.90$. 
D)  $P ( A \curvearrowleft B )$ cannot be determined from the information given.

Question 4

The probability of the union of two mutually exclusive events A and B is P(A $\cup$ B) = P(A) + P(B).

Accepted Answer

A) True 
 B)False

Question 5

Suppose P(A) = 0.25. The probability of complement of A is: $$\begin{array} { | l | l | } 
\hline \text { A. } & 0.25 . \
\hline \text { B. } & 0.50 . \
\hline \text { C. } & - 0.25 \
\hline \text { D. } & 0.75 \
\hline
\end{array}$$

Accepted Answer

The answer of Suppose P(A) = 0.25. The probability of...

Question 6

A survey of a magazine's subscribers indicates that 40% own a home, 80% own a car, and 90% of the homeowners who subscribe also own a car. What proportion of subscribers:
a. own both a car and a house?
b. own a car or a house, or both?
c. own neither a car nor a house?

Accepted Answer

a. 0.36.
b

Question 7

An approach of assigning probabilities that assumes that all outcomes of the experiment are equally likely is referred to as the:

Accepted Answer

A)  subjective approach. 
B)  objective approach. 
C)  classical approach. 
D)  relative frequency approach. 
A)  subjective approach. 
B)  objective approach. 
C)  classical approach. 
D)  relative frequency approach.

Question 8

Suppose P(A) = 0.40, P(B) = 0.50, and P(A $\cap$  B) = 0.70.
a. Find P(A $\cap$  B).
b. Find P(B | A).
c. Are A and B independent events? Explain using probabilities.

Accepted Answer

a. 0.20
b. 0.50
c. Y

Question 9

Suppose P(A) = 0.10, P(B | A) = 0.20, and P(B | $\overline { {A} }$ ) = 0.40.
a. Find P(A$\cap$ B).
b. Are A and B mutually exclusive events?

Accepted Answer

a. 0.02.
b

Question 10

If A and B are independent events, with P(A) = 0.30 and P(B) = 0.50, then P(B | A) is 0.10.

Accepted Answer

A) True 
 B)False

Question 11

If P(A) = 0.65, P(B) =0.76 and P(A $\cap$\ B) =0.80, then P(A $\cup$ B) is: $$\begin{array} { | l | l | } 
\hline \text { A. } & 0.65 . \
\hline \text { B. } & 0.61 . \
\hline \text { C. } & 0.80 . \
\hline \text { D. } & 0.02 . \
\hline
\end{array}$$

Accepted Answer

The answer of If P(A) = 0.65, P(B) =0.76 and...

Question 12

An investment firm has classified its clients according to their gender and the composition of their investment portfolios (primarily bonds, primarily stocks, or a balanced mix of bonds and stocks). The proportions of clients falling into the various categories are shown in the following table:
Portfolio Composition $$\begin{array} { | l | c | c | c | } 
\hline \text { Gender } & \text { Bonds } & \text { Stocks } & \text { Balanced } \
\hline \text { Male } & 0.18 & 0.20 & 0.25 \
\hline \text { Female } & 0.12 & 0.10 & 0.15 \
\hline
\end{array}$$ One client is selected at random, and two events A and B are defined as follows:
A: The client selected is male.
B: The client selected has a balanced portfolio.
Find the following probabilities.
a. P(A $\cup$B).
b. P(A $\cap$ B).
c. P(A $\cap$ $\bar { B }$ ).
d. P( $\bar{A}$$\cup$ $\bar { B }$ ).

Accepted Answer

a. 0.78.
b

Question 13

An investment firm has classified its clients according to their gender and the composition of their investment portfolios (primarily bonds, primarily stocks, or a balanced mix of bonds and stocks). The proportions of clients falling into the various categories are shown in the following table:
Portfolio Composition $$\begin{array} { | l | c | c | c | } 
\hline \text { Gender } & \text { Bonds } & \text { Stocks } & \text { Balanced } \
\hline \text { Male } & 0.18 & 0.20 & 0.25 \
\hline \text { Female } & 0.12 & 0.10 & 0.15 \
\hline
\end{array}$$ One client is selected at random, and two events A and B are defined as follows:
A: The client selected is male.
B: The client selected has a balanced portfolio.
Are A and $\bar { B }$ independent events? Explain.

Accepted Answer

No, since

Question 14

Two events A and B are said to mutually exclusive if: $$\begin{array} { | l | l | } 
\hline \text { A. } & P ( A \mid B ) = 1 . \
\hline \text { B. } & P ( B \mid A ) = 1 \
\hline \text { C. } & P ( A \cap B ) = 1 . \
\hline \text { D. } & P ( A \cap B ) = 0 \
\hline
\end{array}$$

Accepted Answer

The answer of Two events A and B are said...

Question 15

Two events A and B are said to be independent if: $$\begin{array} { | l | l | } 
\hline \text { A. } & P ( A \cap B ) = P ( A ) \times P ( B ) . \
\hline \text { B. } & P ( B \mid A ) = P ( B ) . \
\hline \text { C. } & P ( A \mid B ) = P ( A ) . \
\hline \text { D. } & \text { All of these choices are correct. } \
\hline
\end{array}$$

Accepted Answer

The answer of Two events A and B are said...

Question 16

An investment firm has classified its clients according to their gender and the composition of their investment portfolios (primarily bonds, primarily stocks, or a balanced mix of bonds and stocks). The proportions of clients falling into the various categories are shown in the following table:
Portfolio Composition $$\begin{array} { | l | c | c | c | } 
\hline \text { Gender } & \text { Bonds } & \text { Stocks } & \text { Balanced } \
\hline \text { Male } & 0.18 & 0.20 & 0.25 \
\hline \text { Female } & 0.12 & 0.10 & 0.15 \
\hline
\end{array}$$ One client is selected at random, and two events A and B are defined as follows:
A: The client selected is male.
B: The client selected has a balanced portfolio.
Are A and B independent events? Explain.

Accepted Answer

No, since

Question 17

An ice cream vendor sells three flavours: chocolate, strawberry and vanilla. 45% of the sales are chocolate, 30% are strawberry and the rest are vanilla. Sales are by the cone or the cup. The percentages of cones sales for chocolate, strawberry and vanilla are 75%, 60% and 40%, respectively. For a randomly selected sale, define the following events:
AS1U1B11S1U1B0 = chocolate chosen.
AS1U1B12S1U1B0 = strawberry chosen.
AS1U1B13S1U1B0 = vanilla chosen.
B = ice cream in a cone. $\bar { B }$ = ice cream in a cup.
Use this information to answer the following question(s).
-Find the probability that the ice cream was chocolate-flavoured, given that it was sold on a cone.

Accepted Answer

P( @#LAT-DLM& | B) = P( @#LAT-DLM& @#LAT-DLM& B) /

Question 18

If a coin is tossed three times, and a statistician predicts that the probability of obtaining three heads in a row is 0.125, which of the following assumptions is irrelevant to his prediction?

Accepted Answer

A)  The events are dependent. 
B)  The events are independent. 
C)  The coin is unbiased. 
D)  All of the above assumptions are relevant to his prediction. 
A)  The events are dependent. 
B)  The events are independent. 
C)  The coin is unbiased. 
D)  All of the above assumptions are relevant to his prediction.

Question 19

If A and B are mutually exclusive events, with P(A) = 0.30 and P(B) = 0.40, then P(A $\cup$ B) is:

Accepted Answer

A)  $0.10$. 
B)  $0.12$. 
C)  $0.70$. 
D)  None of these choices are correct. 
A)  $0.10$. 
B)  $0.12$. 
C)  $0.70$. 
D)  None of these choices are correct.

Question 20

An ice cream vendor sells three flavours: chocolate, strawberry and vanilla. 45% of the sales are chocolate, 30% are strawberry and the rest are vanilla. Sales are by the cone or the cup. The percentages of cones sales for chocolate, strawberry and vanilla are 75%, 60% and 40%, respectively. For a randomly selected sale, define the following events:
AS1U1B11S1U1B0 = chocolate chosen.
AS1U1B12S1U1B0 = strawberry chosen.
AS1U1B13S1U1B0 = vanilla chosen.
B = ice cream in a cone. $\bar { B }$ = ice cream in a cup.
Use this information to answer the following question(s).
-Find the probability that the ice cream was sold on a cone.

Accepted Answer

P(B) = P(B @#LAT-DLM& @#LAT-DLM& ) + P(B

A table of joint probabilities is shown below. 0.15 0.25 0.20 0.10 0.15 0.15 Calculate P( $B _ { 2 }$ / $A _ { 1 }$ ).

If P(A) = 0.25 and P(B) = 0.65, then P(A $\cap$ B) is:

The probability of the union of two mutually exclusive events A and B is P(A $\cup$ B) = P(A) + P(B).

Suppose P(A) = 0.25. The probability of complement of A is: A. 0.25. B. 0.50. C. -0.25 D. 0.75

A survey of a magazine's subscribers indicates that 40% own a home, 80% own a car, and 90% of the homeowners who subscribe also own a car. What proportion of subscribers: a. own both a car and a house? b. own a car or a house, or both? c. own neither a car nor a house?

An approach of assigning probabilities that assumes that all outcomes of the experiment are equally likely is referred to as the:

Suppose P(A) = 0.40, P(B) = 0.50, and P(A $\cap$ B) = 0.70. a. Find P(A $\cap$ B). b. Find P(B | A). c. Are A and B independent events? Explain using probabilities.

Suppose P(A) = 0.10, P(B | A) = 0.20, and P(B | $\overline { {A} }$ ) = 0.40. a. Find P(A $\cap$ B). b. Are A and B mutually exclusive events?

If A and B are independent events, with P(A) = 0.30 and P(B) = 0.50, then P(B | A) is 0.10.

If P(A) = 0.65, P(B) =0.76 and P(A $\cap$ \ B) =0.80, then P(A $\cup$ B) is: A. 0.65. B. 0.61. C. 0.80. D. 0.02.

Two events A and B are said to mutually exclusive if: A. P(A\midB)=1. B. P(B\midA)=1 C. P(A\capB)=1. D. P(A\capB)=0

Two events A and B are said to be independent if: A. P(A\capB)=P(A)\timesP(B). B. P(B\midA)=P(B). C. P(A\midB)=P(A). D. All of these choices are correct.

If a coin is tossed three times, and a statistician predicts that the probability of obtaining three heads in a row is 0.125, which of the following assumptions is irrelevant to his prediction?

If A and B are mutually exclusive events, with P(A) = 0.30 and P(B) = 0.40, then P(A $\cup$ B) is:

What Is Statistics

Types of Data, Data Collection and Sampling

Graphical Descriptive Methods Nominal Data

Graphical Descriptive Techniques Numerical Data

Numerical Descriptive Measures

Random Variables and Discrete Probability Distributions

Continuous Probability Distributions

Statistical Inference: Introduction

Sampling Distributions

Estimation: Describing a Single Population

Estimation: Comparing Two Populations

Hypothesis Testing: Describing a Single Population

Hypothesis Testing: Comparing Two Populations

Inference About Population Variances

Analysis of Variance

Additional Tests for Nominal Data: Chi-Squared Tests

Simple Linear Regression and Correlation

Multiple Regression

Model Building

Nonparametric Techniques

Statistical Inference: Conclusion

Time-Series Analysis and Forecasting

Index Numbers

Decision Analysis

Filters

Exam 6: Probability

A table of joint probabilities is shown below. 0.15 0.25 0.20 0.10 0.15 0.15 Calculate P( B2B _ { 2 }B2​ / A1A _ { 1 }A1​ ).

If P(A) = 0.25 and P(B) = 0.65, then P(A ∩\cap∩ B) is:

The probability of the union of two mutually exclusive events A and B is P(A ∪\cup∪ B) = P(A) + P(B).

Suppose P(A) = 0.25. The probability of complement of A is: A. 0.25. B. 0.50. C. -0.25 D. 0.75

A survey of a magazine's subscribers indicates that 40% own a home, 80% own a car, and 90% of the homeowners who subscribe also own a car. What proportion of subscribers: a. own both a car and a house? b. own a car or a house, or both? c. own neither a car nor a house?

An approach of assigning probabilities that assumes that all outcomes of the experiment are equally likely is referred to as the:

Suppose P(A) = 0.40, P(B) = 0.50, and P(A ∩\cap∩ B) = 0.70. a. Find P(A ∩\cap∩ B). b. Find P(B | A). c. Are A and B independent events? Explain using probabilities.

Suppose P(A) = 0.10, P(B | A) = 0.20, and P(B | A‾\overline { {A} }A ) = 0.40. a. Find P(A ∩\cap∩ B). b. Are A and B mutually exclusive events?

If A and B are independent events, with P(A) = 0.30 and P(B) = 0.50, then P(B | A) is 0.10.

If P(A) = 0.65, P(B) =0.76 and P(A ∩\cap∩ \ B) =0.80, then P(A ∪\cup∪ B) is: A. 0.65. B. 0.61. C. 0.80. D. 0.02.

Two events A and B are said to mutually exclusive if: A. P(A\midB)=1. B. P(B\midA)=1 C. P(A\capB)=1. D. P(A\capB)=0

Two events A and B are said to be independent if: A. P(A\capB)=P(A)\timesP(B). B. P(B\midA)=P(B). C. P(A\midB)=P(A). D. All of these choices are correct.

If a coin is tossed three times, and a statistician predicts that the probability of obtaining three heads in a row is 0.125, which of the following assumptions is irrelevant to his prediction?

If A and B are mutually exclusive events, with P(A) = 0.30 and P(B) = 0.40, then P(A ∪\cup∪ B) is:

What Is Statistics

Types of Data, Data Collection and Sampling

Graphical Descriptive Methods Nominal Data

Graphical Descriptive Techniques Numerical Data

Numerical Descriptive Measures

Random Variables and Discrete Probability Distributions

Continuous Probability Distributions

Statistical Inference: Introduction

Sampling Distributions

Estimation: Describing a Single Population

Estimation: Comparing Two Populations

Hypothesis Testing: Describing a Single Population

Hypothesis Testing: Comparing Two Populations

Inference About Population Variances

Analysis of Variance

Additional Tests for Nominal Data: Chi-Squared Tests

Simple Linear Regression and Correlation

Multiple Regression

Model Building

Nonparametric Techniques

Statistical Inference: Conclusion

Time-Series Analysis and Forecasting

Index Numbers

Decision Analysis

Filters

A table of joint probabilities is shown below. 0.15 0.25 0.20 0.10 0.15 0.15 Calculate P( $B _ { 2 }$ / $A _ { 1 }$ ).

If P(A) = 0.25 and P(B) = 0.65, then P(A $\cap$ B) is:

The probability of the union of two mutually exclusive events A and B is P(A $\cup$ B) = P(A) + P(B).

Suppose P(A) = 0.40, P(B) = 0.50, and P(A $\cap$ B) = 0.70. a. Find P(A $\cap$ B). b. Find P(B | A). c. Are A and B independent events? Explain using probabilities.

Suppose P(A) = 0.10, P(B | A) = 0.20, and P(B | $\overline { {A} }$ ) = 0.40. a. Find P(A $\cap$ B). b. Are A and B mutually exclusive events?

If P(A) = 0.65, P(B) =0.76 and P(A $\cap$ \ B) =0.80, then P(A $\cup$ B) is: A. 0.65. B. 0.61. C. 0.80. D. 0.02.

If A and B are mutually exclusive events, with P(A) = 0.30 and P(B) = 0.40, then P(A $\cup$ B) is: