Question 1

You are choosing a region of the country to move to. Let E be the event that the region you choose saw an increase in housing prices of 15% or less, but greater than 10%, and let F be the event that the region you choose is on the east coast.
​  ​
List the outcomes of the event $E \cup F$ as the set of the names of the regions. If the answer is empty set, enter empty.
​ $E \cup F =$ __________
​
List the outcomes of the event $E \cap F$ as the set of the names of the regions. If the answer is empty set, enter empty.
​ $E \cap F =$ __________

Accepted Answer

The answer of You are choosing a region of the...

Question 2

Suppose two dice (one green, one red) are rolled. Consider the following events. A: The red die shows 2. B: The numbers add to 4. C: At least one of the numbers is 2. D: The numbers do not add to 9. Express the following in symbols.
​
"Either the numbers do not add to 4, or they add to 9, or at least one die shows 2".
​
Use the symbol " ~ " for the complement of the event. For example, complement of the event E would be $\sim E$ .

Accepted Answer

The answer of Suppose two dice (one green, one red)...

Question 3

A dime, nickel, and penny are tossed. If we are interested in the number of heads that appear on a single toss, what is the sample space 
 
The sample space is { __________ }.

Accepted Answer

The answer of A dime, nickel, and penny are tossed....

Question 4

Let W be the event that you will use the website tonight, Q be the event that your math grade will improve, and E be the event that you will use the website every night. Express the following event in symbols.
​
"Either your math grade will not improve, or you will use the website tonight, but not every night."
​
Use the symbol " ~ " for the complement of the event. For example, complement of the event E would be $\sim E$ .
​
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Accepted Answer

The answer of Let W be the event that you...

Question 5

The following table shows the results of a survey of authors by a (fictitious) publishing company: $\begin{array}{|l|l|l|l|}
\hline & \text { New Authors } & \begin{array}{l}
\text { Established } \
\text { Authors }
\end{array} & \text { Total } \
\hline \text { Successful } & 5 & 25 & 30 \
\hline \text { Unsuccessful } & 15 & 55 & 70 \
\hline \text { Total } & 20 & 80 & 100 \
\hline
\end{array}$  
Consider the following events:
S: An author is successful; U: An author is unsuccessful; N: An author is new; and E: An author is established.
Are the events N and S mutually exclusive

Accepted Answer

The answer of The following table shows the results of...

Question 6

You are deciding on whether to enroll in Psychology 200, Finite Math 400, Greek Poetry 300, or Calculus 100. Describe the event E of avoiding math classes.

Accepted Answer

The answer of You are deciding on whether to enroll...

Question 7

Let B be the event that you will buy a new car, let A be the event that the car will be an American made car, and let P be the event that you will make payments instead of paying in cash. Express the following in symbols.
​
"You will buy a used car or you will buy an American made car and pay in cash."

Accepted Answer

The answer of Let B be the event that you...

Question 8

The following table shows the results of a survey of authors by a (fictitious) publishing company: $$\begin{array} { | l | l | l | l | } 
\hline & \text { New Authors } & \begin{array} { l } 
\text { Established } \
\text { Authors }
\end{array} & \text { Total } \
\hline \text { Successful } & 5 & 25 & 30 \
\hline \text { Unsuccessful } & 15 & 55 & 70 \
\hline \text { Total } & 20 & 80 & 100 \
\hline
\end{array}$$  
Consider the following events:
S: An author is successful; U: An author is unsuccessful; N: An author is new; and E: An author is established.
Are the events S and N mutually exclusive

Accepted Answer

The answer of The following table shows the results of...

Question 9

Suppose two dice (one green, one red) are rolled. Consider the following events. A: The red die shows 1. B: The numbers add to 6. C: At least one of the numbers is 1. D: The numbers do not add to 11. Express the following in symbols. ​
"The numbers do not add to 6."

Accepted Answer

The answer of Suppose two dice (one green, one red)...

Question 10

Suppose two dice (one green, one red) are rolled. Consider the following events. A: The red die shows 2. B: The numbers add to 6. C: At least one of the numbers is 2. D: The numbers do not add to 11. Express the following in symbols.
​
"Either numbers add to 11 or at least one die shows 2."

Accepted Answer

The answer of Suppose two dice (one green, one red)...

Question 11

A pocket of gummy candy contains 5 strawberry gums, 5 lime gums, 3 black currant gums, and 3 orange gums. April May sticks her hand in and selects 6 at random. April is particularly fond of a combination of 3 strawberry and 3 black currant gums. Complete the following sentence: The event That April May will get the combination she desires is the set of... ​
A)all sets of gummy candies in which 3 are strawberry and 3 black currant.
B) all sets of 6 gummy candies which do not contain lime and orange gummy candies.
C) all sets of 6 gummy candies in which 3 are strawberry and 3 black currant.
D) all sets of 6 gummy candies.
E) all sets of 6 gummy candies which contain strawberry and black currant gummy candies.

Accepted Answer

The event that April May will get the combination she desires is the set of all sets of 6 gummy candies in which 3 are strawberry and 3 black currant. This is because she specifically wants a combination of 3 strawberry and 3 black currant gums, and there may be multiple ways to select 6 candies that do not contain lime and orange gums or that contain any combination of gums. Therefore, the set of all sets of 6 gummy candies in which 3 are strawberry and 3 black currant is the most accurate representation of the desired combination.

Question 12

The following table shows the results of a survey of authors by a (fictitious) publishing company: $\begin{array} { | l | l | l | l | } 
\hline & \text { New Authors } & \begin{array} { l } 
\text { Established } \
\text { Authors }
\end{array} & \text { Total } \
\hline \text { Successful } & 5 & 25 & 30 \
\hline \text { Unsuccessful } & 15 & 55 & 70 \
\hline \text { Total } & 20 & 80 & 100 \
\hline
\end{array}$  
What percentage of new authors are successful  If necessary, round your answer to the nearest hundredth.
__________ %
What percentage of successful authors are new  If necessary, round your answer to the nearest hundredth.
__________ %

Accepted Answer

The answer of The following table shows the results of...

Question 13

My couch potato friend enjoys sitting in front of the TV and grabbing handfuls of five chocolates at random from his snack jar. Unbeknownst to him, I have replaced 1 of the twelve chocolates in his jar with a cashew. (He hates cashews with a passion!)
 
How many possible outcomes are there the first time he grabs five chocolates 
 
How many of these include the cashew

Accepted Answer

The answer of My couch potato friend enjoys sitting in...

Question 14

Let W be the event that you will use the website tonight, Q be the event that your math grade will improve, and E be the event that you will use the website every night. Express the following event in symbols.
​
"Either you will use the website every night, or your math grade will improve."
​
Use the symbol " ~ " for the complement of the event. For example, complement of the event E would be $\sim E$ .

Accepted Answer

The answer of Let W be the event that you...

Question 15

Two dice are rolled. Could there be two mutually exclusive events that both contain outcomes in which the numbers facing up add to 10  If yes, give an example.

Accepted Answer

The answer of Two dice are rolled. Could there be...

Question 16

Two distinguishable dice are rolled. Complete the sentence. ​
There could be two mutually exclusive events that both contain outcomes in which the numbers facing up add to...
​
A)12
B) 11
C) 3
D) 2
E) 8

Accepted Answer

The only way for the numbers on two dice to add up to 3 is for one die to show 1 and the other die to show 2. The two mutually exclusive events would be that the first die shows a 1 or that it doesn't.

Question 17

This table shows the results of a survey of authors by a (fictitious) publishing company $$\begin{array} { | l | l | l | l | } 
\hline & \text { New Authors } & \begin{array} { l } 
\text { Established } \
\text { Authors }
\end{array} & \text { Total } \
\hline \text { Successful } & 5 & 25 & 30 \
\hline \text { Unsuccessful } & 15 & 55 & 70 \
\hline \text { Total } & 20 & 80 & 100 \
\hline
\end{array}$$  
What percentage of established authors are unsuccessful  Express your answer to the nearest hundredth of a percent.
__________%
 
What percentage of unsuccessful authors are established  Express your answer to the nearest hundredth of a percent.
 
__________%

Accepted Answer

The answer of This table shows the results of a...

Quiz 8: Probability

A dime, nickel, and penny are tossed. If we are interested in the number of heads that appear on a single toss, what is the sample space The sample space is { __________ }.

You are deciding on whether to enroll in Psychology 200, Finite Math 400, Greek Poetry 300, or Calculus 100. Describe the event E of avoiding math classes.

Suppose two dice (one green, one red) are rolled. Consider the following events. A: The red die shows 1. B: The numbers add to 6. C: At least one of the numbers is 1. D: The numbers do not add to 11. Express the following in symbols. "The numbers do not add to 6."

Suppose two dice (one green, one red) are rolled. Consider the following events. A: The red die shows 2. B: The numbers add to 6. C: At least one of the numbers is 2. D: The numbers do not add to 11. Express the following in symbols. "Either numbers add to 11 or at least one die shows 2."

Two dice are rolled. Could there be two mutually exclusive events that both contain outcomes in which the numbers facing up add to 10 If yes, give an example.

Two distinguishable dice are rolled. Complete the sentence. There could be two mutually exclusive events that both contain outcomes in which the numbers facing up add to...

Quiz 8: Probability

A dime, nickel, and penny are tossed. If we are interested in the number of heads that appear on a single toss, what is the sample space The sample space is { __________ }.

You are deciding on whether to enroll in Psychology 200, Finite Math 400, Greek Poetry 300, or Calculus 100. Describe the event E of avoiding math classes.

Suppose two dice (one green, one red) are rolled. Consider the following events. A: The red die shows 1. B: The numbers add to 6. C: At least one of the numbers is 1. D: The numbers do not add to 11. Express the following in symbols. ​ "The numbers do not add to 6."

Suppose two dice (one green, one red) are rolled. Consider the following events. A: The red die shows 2. B: The numbers add to 6. C: At least one of the numbers is 2. D: The numbers do not add to 11. Express the following in symbols. ​ "Either numbers add to 11 or at least one die shows 2."

Two dice are rolled. Could there be two mutually exclusive events that both contain outcomes in which the numbers facing up add to 10 If yes, give an example.

Two distinguishable dice are rolled. Complete the sentence. ​ There could be two mutually exclusive events that both contain outcomes in which the numbers facing up add to... ​

Suppose two dice (one green, one red) are rolled. Consider the following events. A: The red die shows 1. B: The numbers add to 6. C: At least one of the numbers is 1. D: The numbers do not add to 11. Express the following in symbols. "The numbers do not add to 6."

Suppose two dice (one green, one red) are rolled. Consider the following events. A: The red die shows 2. B: The numbers add to 6. C: At least one of the numbers is 2. D: The numbers do not add to 11. Express the following in symbols. "Either numbers add to 11 or at least one die shows 2."

Two distinguishable dice are rolled. Complete the sentence. There could be two mutually exclusive events that both contain outcomes in which the numbers facing up add to...