Question 1

A bag of colored candies contains 20 red, 25 yellow, and 35 orange candies. An experiment consists of randomly choosing one candy from the bag and recording its color. What is the sample space for this experiment?
A) {red, yellow, orange}
B) {20, 25, 35}
C) {1/4, 5/16, 7/16}
D) {80}

Accepted Answer

The sample space for this experiment is the set of all possible outcomes, which are the colors of the candies: red, yellow, and orange.

Question 2

A bag of candy was opened and the number of pieces was counted. The results are shown in the table below: $$\begin{array} { l | c } 
\text { Color } & \text { Number } \
\hline \text { Red } & 25 \
\text { Brown } & 20 \
\text { Green } & 20 \
\text { Blue } & 15 \
\text { Yellow } & 10 \
\text { Orange } & 10
\end{array}$$ Find the probability that a randomly chosen piece of candy is not blue or red.
A) 0.40
B) 0.85
C) 0.15
D) 0.60

Accepted Answer

The total number of candies is 100. The number of candies that are not blue or red is 60 (20 brown + 20 green + 10 yellow + 10 orange). The probability is 60/100 = 0.60.

Question 3

Fill in the blank. A(n) ______ is a process that leads to a single outcome that cannot be predicted with certainty.
A) experiment
B) event
C) sample point
D) sample space

Accepted Answer

An experiment is a process that leads to a single outcome that cannot be predicted with certainty.

Question 4

In any experiment with exactly four sample points in the sample space, the probability of each sample point is .25.

Accepted Answer

The probability of each sample point in a sample space depends on the specific experiment and how the sample points are defined. It is not necessarily true that each sample point has a probability of .25 in a sample space with exactly four sample points; the probabilities can vary as long as they sum up to 1.

Question 5

Which number could be the probability of an event that rarely occurs?
A) .01
B) -.01
C) .51
D) .99

Accepted Answer

.01 is a probability of an event that rarely occurs.

Question 6

An experiment consists of randomly choosing a number between 1 and 10. Let E be the event that the number chosen is even. List the sample points in E.
A) {2, 4, 6, 8, 10}
B) {1, 2, 3, 4, 5, 6, 7, 8, 9, 10}
C) {1, 3, 5, 7, 9}
D) {5}

Accepted Answer

The even numbers between 1 and 10 are 2, 4, 6, 8, and 10.

Question 7

Which of the following assignments of probabilities to the sample points A, B, and C is valid if A, B, and C are the only sample points in the experiment? A) $P ( A ) = 0 , P ( B ) = \frac { 1 } { 12 } , P ( C ) = \frac { 11 } { 12 }$

B) $P ( A ) = \frac { 1 } { 7 } , P ( B ) = \frac { 1 } { 2 } , P ( C ) = \frac { 1 } { 8 }$

C) $P ( A ) = - \frac { 1 } { 4 } , P ( B ) = \frac { 1 } { 2 } , P ( C ) = \frac { 3 } { 4 }$

D) $P ( A ) = \frac { 1 } { 4 } , P ( B ) = \frac { 1 } { 4 } , P ( C ) = \frac { 1 } { 4 }$

Accepted Answer

The answer of Which of the following assignments of probabilities...

Question 8

An experiment consists of rolling two dice and summing the resulting values. Which of the following is not a sample point for this experiment?
A) 1
B) 2
C) 6
D) 7

Accepted Answer

The smallest sum possible when rolling two dice is 2 (1+1), so 1 is not a possible outcome.

Question 9

A statistical experiment can be almost any act of observation as long as the outcome is uncertain.

Accepted Answer

A statistical experiment involves randomly selecting individuals, assigning treatments, and observing responses to determine the effects of the treatments. The outcome of the experiment is uncertain, so any act of observation that involves uncertainty can be considered a statistical experiment.

Question 10

The outcome of an experiment is the number of resulting heads when a nickel and a dime are flipped simultaneously. What is the sample space for this experiment?
A) {0, 1, 2}
B) {HH, HT, TT}
C) {HH, HT, TH, TT}
D) {nickel, dime}

Accepted Answer

The answer of The outcome of an experiment is the...

Question 11

Which number could be the probability of an event that occurs about as often as it does not occur?
A) .51
B) -.51
C) 0
D) 1

Accepted Answer

A probability of .51 indicates that the event occurs slightly more often than it does not, which is close to an even chance.

Question 12

Suppose that an experiment has five equally likely outcomes. What probability is assigned to each of the sample points?
A) .2
B) .5
C) .05
D) 1

Accepted Answer

In an experiment with equally likely outcomes, the probability of each outcome is 1 divided by the number of outcomes. Here, 1/5 = 0.2.

Question 13

A bag of candy was opened and the number of pieces was counted. The results are shown in the table below: $$\begin{array} { l | c } 
\text { Color } & \text { Number } \
\hline \text { Red } & 25 \
\text { Brown } & 20 \
\text { Green } & 20 \
\text { Blue } & 15 \
\text { Yellow } & 10 \
\text { Orange } & 10
\end{array}$$ List the sample space for this problem.
A) {25, 20, 20, 15, 10, 10}
B) {0.25, 0.20, 0.20, 0.15, 0.10, 0.10}
C) {Red, Brown, Green, Blue, Yellow, Orange}
D) {Red}

Accepted Answer

The sample space consists of all possible outcomes, which in this case are the colors of the candy pieces.

Question 14

Which number could be the probability of an event that is almost certain to occur?
A) .99
B) 1.01
C) .51
D) .01

Accepted Answer

A probability of .99 indicates an event that is almost certain to occur, as probabilities range from 0 to 1.

Question 15

If sample points A, B, C, and D are the only possible outcomes of an experiment, find the probability of D using the table below. . $\begin{array}{l|cccc}
\text { Sample Point } & A & B & C & D \
\hline \text { Probability } & 1 / 11 & 1 / 11 & 1 / 11 &
\end{array}$

A) $\frac { 8 } { 11 }$

B) $\frac { 1 } { 11 }$

C) $\frac { 1 } { 4 }$

D) $\frac { 3 } { 11 }$

Accepted Answer

The answer of If sample points A, B, C, and...

Question 16

Fill in the blank. A(n) __________ is the most basic outcome of an experiment.
A) sample point
B) event
C) experiment
D) sample space

Accepted Answer

A sample point is the most basic outcome of an experiment, representing a single possible result.

Question 17

The probability of a sample point is usually taken to be the relative frequency of the occurrence of the sample point in a very long series of repetitions of the experiment.

Accepted Answer

This is the definition of probability based on the frequentist interpretation.

Question 18

Fill in the blank. A(n) __________ is a collection of sample points.
A) event
B) Venn diagram
C) sample space
D) experiment

Accepted Answer

An event is a collection of sample points, which are the possible outcomes of an experiment.

Question 19

Fill in the blank. The __________ is the collection of all the sample points in an experiment.
A) sample space
B) Venn diagram
C) event
D) union

Accepted Answer

The sample space is the collection of all possible outcomes or sample points in an experiment.

Question 20

In some experiments, we assign subjective probabilities, which can be interpreted as our degree of belief in the outcome.

Accepted Answer

Yes, in Bayesian statistics, subjective probabilities represent our degree of belief in the outcome based on available evidence. This is different from frequentist statistics, which rely on objective probabilities that are observed over many repeated trials.

Quiz 3: Probability

A bag of colored candies contains 20 red, 25 yellow, and 35 orange candies. An experiment consists of randomly choosing one candy from the bag and recording its color. What is the sample space for this experiment?

Fill in the blank. A(n) ______ is a process that leads to a single outcome that cannot be predicted with certainty.

In any experiment with exactly four sample points in the sample space, the probability of each sample point is .25.

Which number could be the probability of an event that rarely occurs?

An experiment consists of randomly choosing a number between 1 and 10. Let E be the event that the number chosen is even. List the sample points in E.

An experiment consists of rolling two dice and summing the resulting values. Which of the following is not a sample point for this experiment?

A statistical experiment can be almost any act of observation as long as the outcome is uncertain.

The outcome of an experiment is the number of resulting heads when a nickel and a dime are flipped simultaneously. What is the sample space for this experiment?

Which number could be the probability of an event that occurs about as often as it does not occur?

Suppose that an experiment has five equally likely outcomes. What probability is assigned to each of the sample points?

Which number could be the probability of an event that is almost certain to occur?

Fill in the blank. A(n) __________ is the most basic outcome of an experiment.

The probability of a sample point is usually taken to be the relative frequency of the occurrence of the sample point in a very long series of repetitions of the experiment.

Fill in the blank. A(n) __________ is a collection of sample points.

Fill in the blank. The __________ is the collection of all the sample points in an experiment.

In some experiments, we assign subjective probabilities, which can be interpreted as our degree of belief in the outcome.