Question 1

When events are mutually exclusive, they can happen at the same time.

Accepted Answer

A) True 
 B)False  False

Question 2

The collection of all possible outcomes of an experiment is called:

Accepted Answer

A)  a simple event. 
B)  a sample space. 
C)  a sample. 
D)  a population. 
A)  a simple event. 
B)  a sample space. 
C)  a sample. 
D)  a population. B

Question 3

Five students from a statistics class have formed a study group. Each may or may not attend a study session. Assuming that the members will be making independent decisions on whether or not to attend, there are 32 different possibilities for the composition of the study session.

Accepted Answer

A) True 
 B)False  True

Question 4

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( $A _ { 1 }$ | $B _ { 2 }$ ).

Accepted Answer

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

Question 5

If an experiment consists of five outcomes, with $P \left( O _ { 1 } \right) =$ 0.10, $P \left( O _ { 2 } \right) =$ 0.10, $P \left( O _ { 3 } \right) =$ 0.30, $P \left( O _ { 4 } \right) =$ 0.25, then $P \left( O _ { s } \right)$ is: $$\begin{array} { | l | l | } 
\hline \text { A. } & 0.75 . \
\hline \text { B. } & 0.25 . \
\hline \text { C. } & 0.20 . \
\hline \text { D. } & 0.80 . \
\hline
\end{array}$$

Accepted Answer

The answer of If an experiment consists of five outcomes,...

Question 6

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( $A _ { 1 }$ | $B _ { 1 }$ ).

Accepted Answer

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

Question 7

Which of the following is a requirement of the probabilities assigned to the outcomes $$O _ { i }$$

Accepted Answer

A)  $P\left(O_{i}\right) \leq 0$ 
B)  $P\left(O_{i}\right) \geq 0$ 
C)  $0 \leq P\left(O_{i}\right) \leq 0, \text { for each } i$ 
D)  $P\left(O_{i}\right)=1+P\left(\bar{C}_{i}\right)$ 
A)  $P\left(O_{i}\right) \leq 0$ 
B)  $P\left(O_{i}\right) \geq 0$ 
C)  $0 \leq P\left(O_{i}\right) \leq 0, \text { for each } i$ 
D)  $P\left(O_{i}\right)=1+P\left(\bar{C}_{i}\right)$

Question 8

If A and B are independent events with P(A) = 0.60 and P(A/B) = 0.60, then P(B) is:

Accepted Answer

A)  $1.20$. 
B)  $0.60$. 
C)  $0.36$. 
D)  $P ( B )$ cannot be determined with the information given. 
A)  $1.20$. 
B)  $0.60$. 
C)  $0.36$. 
D)  $P ( B )$ cannot be determined with the information given.

Question 9

Which of the following statements is always correct? $$\begin{array} { l l } 
\text { A. } & P ( A \frown B ) = P ( A ) \times P ( B ) \
\hline \text { B. } & P ( A \cup B ) = P ( A ) + P ( B ) \
\hline \text { C. } & P ( A \cup B ) = P ( A ) + P ( B ) + P ( A \frown B ) \
\hline \text { D. } & P ( A ) = 1 - P ( A ) \
\hline
\end{array}$$

Accepted Answer

The answer of Which of the following statements is always...

Question 10

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 strawberry-flavoured, given that it was sold on a cone.

Accepted Answer

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

Question 11

Is it possible to have two events for which P(A) = 0.40, P(B) = 0.50, and P(A$\cup$B) = 0.20? Explain.

Accepted Answer

No, since P(A @#LAT-DLM& B) mu

Question 12

If the events A and B are independent, with P(A) = 0.30 and P(B) = 0.40, then the probability that both events will occur simultaneously is: $$\begin{array} { | l | l | } 
\hline \text { A. } & 0.10 . \
\hline \text { B. } & 0.12 . \
\hline \text { C. } & 0.70 \
\hline \text { D. } & 0.75 \
\hline
\end{array}$$

Accepted Answer

The answer of If the events A and B are...

Question 13

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( $A _ { 1 }$ $\cup$ $B _ { 1 }$ ).

Accepted Answer

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

Question 14

Three candidates for the presidency of a university's student union, Alice, Brenda and Cameron, are to address a student forum. The forum's organiser is to select the order in which the candidates will give their speeches, and must do so in such a way that each possible order is equally likely to be selected.
a. What is the random experiment?
b. List the simple events in the sample space.
c. Assign probabilities to the simple events.
d. What is the probability that Cameron will speak first?
e. What is the probability that one of the women will speak first?
f. What is the probability that Alice will speak before Cameron does?

Accepted Answer

a. The random experiment is to observe t

Question 15

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 and the flavour was:
a. chocolate.
b. strawberry.
c. vanilla.

Accepted Answer

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

Question 16

If A and B are mutually exclusive events with P(A) = 0.80, then P(B):

Accepted Answer

A)  Can take any value between 0 and $1 .$ 
B)  Can take any value between 0 and $0.80$. 
C)  Can be larger than $0.80$. 
D)  Cannot be larger than $0.20$. 
A)  Can take any value between 0 and $1 .$ 
B)  Can take any value between 0 and $0.80$. 
C)  Can be larger than $0.80$. 
D)  Cannot be larger than $0.20$.

Question 17

If P(A) = 0.35, P(B) = 0.45 and P(A $\cap$\ B) =0.20, then P(A | B) is: $$\begin{array} { | l | l | } 
\hline \text { A. } & 0.80 . \
\hline \text { B. } & 0.60 . \
\hline \text { C. } & 0.44 . \
\hline \text { D. } & 0.57 . \
\hline
\end{array}$$

Accepted Answer

The answer of If P(A) = 0.35, P(B) = 0.45...

Question 18

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( $A _ { 1 }$ / $A _ { 2 }$ ).

Accepted Answer

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

Question 19

Marginal probability is the probability that a given event will occur, with no other events taken into consideration.

Accepted Answer

A) True 
 B)False

Question 20

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

Accepted Answer

A) True 
 B)False

Exam 6: Probability

When events are mutually exclusive, they can happen at the same time.

The collection of all possible outcomes of an experiment is called:

Five students from a statistics class have formed a study group. Each may or may not attend a study session. Assuming that the members will be making independent decisions on whether or not to attend, there are 32 different possibilities for the composition of the study session.

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

A table of joint probabilities is shown below. 0.15 0.25 0.20 0.10 0.15 0.15 Calculate P( A1A _ { 1 }A1​ | B1B _ { 1 }B1​ ).

Which of the following is a requirement of the probabilities assigned to the outcomes OiO _ { i }Oi​

If A and B are independent events with P(A) = 0.60 and P(A/B) = 0.60, then P(B) is:

Which of the following statements is always correct? A. P(A\frownB)=P(A)\timesP(B) B. P(A\cupB)=P(A)+P(B) C. P(A\cupB)=P(A)+P(B)+P(A\frownB) D. P(A)=1-P(A)

Is it possible to have two events for which P(A) = 0.40, P(B) = 0.50, and P(A ∪\cup∪ B) = 0.20? Explain.

If the events A and B are independent, with P(A) = 0.30 and P(B) = 0.40, then the probability that both events will occur simultaneously is: A. 0.10. B. 0.12. C. 0.70 D. 0.75

A table of joint probabilities is shown below. 0.15 0.25 0.20 0.10 0.15 0.15 Calculate P( A1A _ { 1 }A1​ ∪\cup∪ B1B _ { 1 }B1​ ).

If A and B are mutually exclusive events with P(A) = 0.80, then P(B):

If P(A) = 0.35, P(B) = 0.45 and P(A ∩\cap∩ \ B) =0.20, then P(A | B) is: A. 0.80. B. 0.60. C. 0.44. D. 0.57.

A table of joint probabilities is shown below. 0.15 0.25 0.20 0.10 0.15 0.15 Calculate P( A1A _ { 1 }A1​ / A2A _ { 2 }A2​ ).

Marginal probability is the probability that a given event will occur, with no other events taken into consideration.

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

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( $A _ { 1 }$ | $B _ { 2 }$ ).

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

Which of the following is a requirement of the probabilities assigned to the outcomes $O _ { i }$

Is it possible to have two events for which P(A) = 0.40, P(B) = 0.50, and P(A $\cup$ B) = 0.20? Explain.

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

If P(A) = 0.35, P(B) = 0.45 and P(A $\cap$ \ B) =0.20, then P(A | B) is: A. 0.80. B. 0.60. C. 0.44. D. 0.57.

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