Question 1

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

Accepted Answer

A) P(Oi) F1F1F1S1?F1F1F10 0. 
B) P(Oi) F1F1F1S1?F1F1F10 0. 
C) 0 F1F1F1S1?F1F1F10 P(Oi) F1F1F1S1?F1F1F10 0, for each i. 
D) P(Oi) = 1 + P( $\bar { O } _ { i }$ ). 
A) P(Oi) F1F1F1S1?F1F1F10 0. 
B) P(Oi) F1F1F1S1?F1F1F10 0. 
C) 0 F1F1F1S1?F1F1F10 P(Oi) F1F1F1S1?F1F1F10 0, for each i. 
D) P(Oi) = 1 + P( $\bar { O } _ { i }$ ). C

Question 2

Suppose P(A) = 0.50, P(B) = 0.30, and P(A or B) = 0.80. 
a. Find $P ( A \cap B )$
b. Find $P ( B \mid A )$
c. Are A and B mutually exclusive events? Explain using probabilities.

Accepted Answer

a. 0.0.
b. 0.0.
c. Yes, since P(A F1F1F1S1F1F1F10 B) = 0.

Question 3

If you roll a fair (unbiased) die 60 times, you should expect an odd number to appear:

Accepted Answer

A) in each of the first 30 rolls. 
B) 30 out of the 60 rolls. 
C) on every other roll. 
D) 40 out of the 60 rolls. 
A) in each of the first 30 rolls. 
B) 30 out of the 60 rolls. 
C) on every other roll. 
D) 40 out of the 60 rolls. B

Question 4

A law firm has submitted bids on two separate state contracts, A and B.The company feels that it has a 40% chance of winning contract A, and a 60% chance of winning contract B.Furthermore, the company believes that it has a 75% chance of winning contract B, given that it wins contract A. If the firm wins contract A, what is the probability that it will not win contract B?

Accepted Answer

The answer of A law firm has submitted bids on...

Question 5

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 6

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. $P ( A \mid B )$
b. $P ( B \mid A )$
c. $P ( A \mid \bar { B } )$
d. $P ( \bar { A } \mid B )$

Accepted Answer

a. 0.625.

Question 7

Suppose P(A) = 0.30, P(B) = 0.40, and P(B /A) = 0.60.
a. Find P(A F1F1F1S1F1F1F10 B).
b. Find P(A F1F1F1S1F1F1F10 B).
c. Find P(A /B).

Accepted Answer

a. 0.18.
b

Question 8

A law firm has submitted bids on two separate state contracts, A and B.The company feels that it has a 40% chance of winning contract A, and a 60% chance of winning contract B.Furthermore, the company believes that it has a 75% chance of winning contract B, given that it wins contract A.What is the probability that the firm will win at least one of the two contracts?

Accepted Answer

The answer of A law firm has submitted bids on...

Question 9

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. $\quad P ( A \cup B )$.
b. $P ( A \cap B )$.
c. $P ( A \cap \bar { B } )$.
d. $\quad P ( \bar { A } \cup \bar { B } )$.

Accepted Answer

a. 0.78.
b

Question 10

Find the probability that the ice cream was sold in a cup.

Accepted Answer

P( @#IMG-DLM& ) = 1

Question 11

Which of the following statements is always correct?

Accepted Answer

A) P(A F1F1F1S1?F1F1F10 
B)  = P(
A)  F1F1F1S1?F1F1F10 P(
B) . 
B) P(A F1F1F1S1?F1F1F10 
B)  = P(
A)  + P(
B) . 
C) P(A F1F1F1S1?F1F1F10 
B)  = P(
A)  + P(
B)  + P(A F1F1F1S1?F1F1F10 
B) . 
D) P(
A)  = 1 - P( $\bar { A }$ ). 
A) P(A F1F1F1S1?F1F1F10 
B)  = P(
A)  F1F1F1S1?F1F1F10 P(
B) . 
B) P(A F1F1F1S1?F1F1F10 
B)  = P(
A)  + P(
B) . 
C) P(A F1F1F1S1?F1F1F10 
B)  = P(
A)  + P(
B)  + P(A F1F1F1S1?F1F1F10 
B) . 
D) P(
A)  = 1 - P( $\bar { A }$ ).

Question 12

An insurance company has recently recruited ten graduates, four men and six women. Two of the graduates are to be selected at random to work in the firm's suburban office.
a. What is the probability that two men will be selected?
b. What is the probability that at least one man will be selected?

Accepted Answer

The answer of An insurance company has recently recruited ten...

Question 13

If we wished to determine the probability that one or more of several events will occur in an experiment, we would use addition rules.

Accepted Answer

A) True 
 B)False

Question 14

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

Accepted Answer

a. 0.02.
b. No, beca

Question 15

Two or more events are said to be independent when the occurrence of one event has an effect on the probability that another will occur.

Accepted Answer

A) True 
 B)False

Question 16

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 17

When a fair die is rolled once, the sample space consists of the following six outcomes: 1, 2, 3, 4, 5, 6. Given this sample space, which of the following is a simple event?

Accepted Answer

A) Even number. 
B) More than 4. 
C) Less than 1. 
D) 4. 
A) Even number. 
B) More than 4. 
C) Less than 1. 
D) 4.

Question 18

If A and B are mutually exclusive events, with P(A) = 0.30 and P(B) = 0.40, then P(A F1F1F1S1F1F1F10 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 19

The probability of the union of two mutually exclusive events A and B is P(A F1F1F1S1F1F1F10 B) = P(A) + P(B).

Accepted Answer

A) True 
 B)False

Question 20

A pharmaceutical firm has discovered a new diagnostic test for a certain disease that has infected 1% of the population. The firm has announced that 95% of those infected will show a positive test result, while 98% of those not infected will show a negative test result. What proportion of test results are correct?

Accepted Answer

The answer of A pharmaceutical firm has discovered a new...

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

Suppose P(A) = 0.50, P(B) = 0.30, and P(A or B) = 0.80. a. Find $P ( A \cap B )$ b. Find $P ( B \mid A )$ c. Are A and B mutually exclusive events? Explain using probabilities.

If you roll a fair (unbiased) die 60 times, you should expect an odd number to appear:

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

Suppose P(A) = 0.30, P(B) = 0.40, and P(B /A) = 0.60. a. Find P(A  B). b. Find P(A  B). c. Find P(A /B).

Find the probability that the ice cream was sold in a cup.

Which of the following statements is always correct?

An insurance company has recently recruited ten graduates, four men and six women. Two of the graduates are to be selected at random to work in the firm's suburban office. a. What is the probability that two men will be selected? b. What is the probability that at least one man will be selected?

If we wished to determine the probability that one or more of several events will occur in an experiment, we would use addition rules.

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

Two or more events are said to be independent when the occurrence of one event has an effect on the probability that another will occur.

When a fair die is rolled once, the sample space consists of the following six outcomes: 1, 2, 3, 4, 5, 6. Given this sample space, which of the following is a simple event?

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

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

What Is Statistics

Types of Data, Data Collection and Sampling

Graphical Descriptive Techniques Nominal Data

Graphical Descriptive Techniques Numerical Data

Numerical Descriptive Measures

Random Variables and Discrete Probability Distributions

Continuous Probability Distributions

Statistical Inference and Sampling Distributions

Estimation: Describing a Single Population

Estimation: Comparing Two Populations

Hypothesis Testing: Describing a Single Population

Hypothesis Testing: Comparing Two Populations

Additional Tests for Nominal Data: Chi-Squared Tests

Simple Linear Regression and Correlation

Multiple Regression

Time-Series Analysis and Forecasting

Index Numbers

Filters

Exam 6: Probability

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

Suppose P(A) = 0.50, P(B) = 0.30, and P(A or B) = 0.80. a. Find P(A∩B)P ( A \cap B )P(A∩B) b. Find P(B∣A)P ( B \mid A )P(B∣A) c. Are A and B mutually exclusive events? Explain using probabilities.

If you roll a fair (unbiased) die 60 times, you should expect an odd number to appear:

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

Suppose P(A) = 0.30, P(B) = 0.40, and P(B /A) = 0.60. a. Find P(A  B). b. Find P(A  B). c. Find P(A /B).

Find the probability that the ice cream was sold in a cup.

Which of the following statements is always correct?

An insurance company has recently recruited ten graduates, four men and six women. Two of the graduates are to be selected at random to work in the firm's suburban office. a. What is the probability that two men will be selected? b. What is the probability that at least one man will be selected?

If we wished to determine the probability that one or more of several events will occur in an experiment, we would use addition rules.

Suppose P(A)=0.10,P(B∣A)=0.20, and P(B∣Aˉ)=0.40P ( A ) = 0.10 , P ( B \mid A ) = 0.20 , \text { and } P ( B \mid \bar { A } ) = 0.40P(A)=0.10,P(B∣A)=0.20, and P(B∣Aˉ)=0.40 a. Find P(A∩B)P ( A \cap B )P(A∩B) b. Are A and B mutually exclusive events

Two or more events are said to be independent when the occurrence of one event has an effect on the probability that another will occur.

When a fair die is rolled once, the sample space consists of the following six outcomes: 1, 2, 3, 4, 5, 6. Given this sample space, which of the following is a simple event?

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

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

What Is Statistics

Types of Data, Data Collection and Sampling

Graphical Descriptive Techniques Nominal Data

Graphical Descriptive Techniques Numerical Data

Numerical Descriptive Measures

Random Variables and Discrete Probability Distributions

Continuous Probability Distributions

Statistical Inference and Sampling Distributions

Estimation: Describing a Single Population

Estimation: Comparing Two Populations

Hypothesis Testing: Describing a Single Population

Hypothesis Testing: Comparing Two Populations

Additional Tests for Nominal Data: Chi-Squared Tests

Simple Linear Regression and Correlation

Multiple Regression

Time-Series Analysis and Forecasting

Index Numbers

Filters

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

Suppose P(A) = 0.50, P(B) = 0.30, and P(A or B) = 0.80. a. Find $P ( A \cap B )$ b. Find $P ( B \mid A )$ c. Are A and B mutually exclusive events? Explain using probabilities.

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