Question 1

A coin is tossed 758 times and comes up heads 409 times. Use the Empirical Method to approximate the probability that the coin comes up heads.

Accepted Answer

The Empirical Method approximates the probability of an event by dividing the number of times the event occurs by the total number of trials. Here, heads came up 409 times out of 758 tosses, so the probability is 409/758 ≈ 0.54.

Question 2

A survey asked 34,407 homeowners how many pets they owned. The results were as follc
$\begin{array}{cc}
\hline \text { Number of Pets } & \text { Number of Homeowners } \
\hline 0 & 6120 \
1 & 11,915 \
2 & 9360 \
3 & 6363 \
4 \text { or more } & 649 \
\hline \text { Total } & 34,407
\end{array}$
What is the probability that a sampled homeowner has more than 1 pet? wed:

Accepted Answer

The probability that a sampled homeowner has more than 1 pet is found by adding the number of homeowners with more than 1 pet (2 pets, 3 pets, and 4 or more pets) and dividing by the total number of homeowners. This gives (9360 + 6363 + 649) / 34,407 = 16,372 / 34,407 ≈ 0.476.

Question 3

The arrow on the spinner shown below can be spun so that the arrowhead eventually stops in one of the three sectors labeled "A", "B", or "C". The spinner is spun 124 times and comes up "A" 52 times. Use the Empirical Rule to approximate the probability that tl spinner comes up "A".

Accepted Answer

The answer of The arrow on the spinner shown below...

Question 4

There are 27,842 undergraduate students enrolled at a certain university. The age distribution is as follows:
$\begin{array}{cc}
\hline \text { Age Range } & \text { Number } \
\hline 13-14 & 2 \
15-17 & 49 \
18-22 & 11,563 \
23-30 & 9568 \
31 \text { and up } & 6660 \
\hline \text { Total } & 27,842
\end{array}$
What is the probability that a student is between 23 and 30 years old?

Accepted Answer

The probability that a student is between 23 and 30 years old is calculated by dividing the number of students in that age range (9,568) by the total number of students (27,842). This gives $ \frac{9568}{27842} \approx 0.344 $.

Question 5

At a certain college, there were 700 science majors, 300 engineering majors, and business majors. If one student was selected at random, the probability that the student
Is an engineering major is

Accepted Answer

The total number of students is not given directly, but we can calculate it as 700 (science majors) + 300 (engineering majors) + business majors (not specified). The probability of selecting an engineering major is the number of engineering majors divided by the total number of students. Without the number of business majors, we cannot calculate the exact probability, but the correct form of expressing the probability of selecting an engineering major from the given options is $\frac{1}{5}$, assuming the missing information does not alter the proportions significantly.

Question 6

At Wassamatta University, 59.3% of the student body are males. Choose one student at random. What is the probability that the student is female?

Accepted Answer

Since 59.3% of the students are males, the remaining 100% - 59.3% = 40.7% must be females. Therefore, the probability of randomly selecting a female student is 40.7%.

Question 7

Box A contains the numbers $1,2,3$, and 4 . Box B contains the numbers $5,6,7$, and $8 . \mathrm { A } _ { 1 }$ first drawn from Box A and then another number from Box B. Using the figure below, ho outcomes are possible if both numbers are even?

umber is

Accepted Answer

The answer of Box A contains the numbers $1,2,3$, and...

Question 8

A Karate club consists of 41 persons holding a black belt (highest rating), 59 persons holding a brown belt (middle rating), and 73 persons holding a purple belt (lowest
Rating). What is the probability that a randomly-selected club member holds a brown belt
Or a purple belt?

Accepted Answer

The answer of A Karate club consists of 41 persons...

Question 9

A Karate club consists of 52 persons holding a black belt (highest rating), 69 persons holding a brown belt (middle rating), and 83 persons holding a purple belt (lowest
Rating). What is the probability that a randomly-selected club member holds a black belt?

Accepted Answer

The probability is calculated by dividing the number of black belt holders by the total number of club members: 52 / (52 + 69 + 83) = 52 / 204 = 0.255.

Question 10

A survey asked respondents to indicate their level of satisfaction with government spending. The results are show below.
$\begin{array}{cc}
\hline \text { Response } & \text { Number } \
\hline \text { Very satisfied } & 774 \
\text { Somewhat satisfied } & 3959 \
\text { Dissatisfied } & 7668 \
\hline \text { Total } & 12,401
\end{array}$
Assume this is a simple random sample from a population. Use the Empirical Method to ، the probability that a person is dissatisfied with government's spending?

Accepted Answer

The probability is calculated by dividing the number of dissatisfied respondents by the total number of respondents: 7668 / 12401 = 0.618.

Question 11

A probability experiment has two steps. There are two possible results for the first step, call them "A" and "B". If the result for the first step was "A", then there would be 5
Possible results for the second step. If the result for the first step was "B", then there
Would be 12 possible results for the second step. How many possible outcomes are there
For this experiment?

Accepted Answer

The total number of possible outcomes is the sum of the outcomes from each branch of the first step: 5 outcomes when the first step is "A" and 12 outcomes when the first step is "B". Therefore, the total number of possible outcomes is 5 + 12 = 17.

Question 12

A survey asked 32,901 homeowners how many pets they owned. The results were as follc
$\begin{array}{cc}
\hline \text { Number of Pets } & \text { Number of Homeowners } \
\hline 0 & 6316 \
1 & 9709 \
2 & 9627 \
3 & 6618 \
4 \text { or more } & 631 \
\hline \text { Total } & 32,901
\end{array}$
Assume this is a simple random sample of homeowners. Use the Empirical Method to estimate the probability that a homeowner has at least one pet. wed:

Accepted Answer

To estimate the probability that a homeowner has at least one pet, subtract the number of homeowners with 0 pets from the total number of homeowners, then divide by the total number of homeowners. $ \frac{32901 - 6316}{32901} = \frac{26585}{32901} \approx 0.808 $.

Question 13

So far this season, the university's football team has executed 145 running plays, 149 passing plays, and 24 "trick" plays. What is the probability that the team will execute a
Passing play?

Accepted Answer

The probability of the team executing a passing play is 149/318, which is approximately 0.469.

Question 14

A survey asked 32,011 homeowners how many pets they owned. The results were as follc
$\begin{array}{cc}
\hline \text { Number of Pets } & \text { Number of Homeowners } \
\hline 0 & 5583 \
1 & 10,423 \
2 & 8856 \
3 & 6349 \
4 \text { or more } & 800 \
\hline \text { Total } & 32,011
\end{array}$
What is the probability that a sampled homeowner has three pets? wed:

Accepted Answer

The probability that a sampled homeowner has three pets is calculated by dividing the number of homeowners with three pets by the total number of homeowners surveyed. This gives $ \frac{6349}{32011} \approx 0.198 $.

Question 15

In a recent study, the following responses were obtained to the question, "Do you favor re in your neighborhood?"
$\begin{array}{llll} 
& \frac{\text { Yes }}{} & \frac{\text { No }}{} & \frac{\text { No Opinion }}{} \
\text { Males } & 25 & 15 & 10 \
\text { Females } & 30 & 10 & 10
\end{array}$
If a response is picked at random, what is the probability that it came from a male or that indicated no opinion regarding recycling?

Accepted Answer

The total number of responses is 100 (25+15+10+30+10+10). The number of male responses is 50 (25+15+10), and the number of no opinion responses is 20 (10+10). The probability of picking a response from a male or with no opinion is the sum of the probabilities of each, minus the overlap (which is the no opinion from males, already counted in the male total), so $ \frac{50 + 20 - 10}{100} = \frac{60}{100} = \frac{3}{5} $.

Question 16

The staff at a small company includes: 4 secretaries, 20 technicians, 4 engineers, 2 executives, and 50 factory workers. If a person is selected at random, what is the
Probability that he or she is a factory worker?

Accepted Answer

The total number of staff is 4 + 20 + 4 + 2 + 50 = 80. The probability of selecting a factory worker is the number of factory workers divided by the total number of staff, which is 50/80 = 5/8.

Question 17

There are 28,446 undergraduate students enrolled at a certain university. The age distribut is as follows:
$\begin{array}{cc}
\hline \text { Age Range } & \text { Number } \
\hline 13-14 & 5 \
15-17 & 434 \
18-22 & 12,057 \
23-30 & 9256 \
31 \text { and up } & 6694 \
\hline \text { Total } & 28,446
\end{array}$
What is the probability that a student is less than 18 years old? n

Accepted Answer

The probability is calculated by dividing the number of students less than 18 years old (5 + 434 = 439) by the total number of students (28,446). Thus, the probability is 439/28,446 ≈ 0.0154.

Question 18

A survey asked respondents to indicate their level of satisfaction with government spending. The results are show below.
$\begin{array}{cc}
\hline \text { Response } & \text { Number } \
\hline \text { Very satisfied } & 599 \
\text { Somewhat satisfied } & 4694 \
\text { Dissatisfied } & 7410 \
\hline \text { Total } & 12,703
\end{array}$
What is the probability that a sampled person was only somewhat satisfied or dissatisfied government's spending?

Accepted Answer

The probability is calculated by adding the number of people who were "somewhat satisfied" (4694) and "dissatisfied" (7410) and then dividing by the total number of respondents (12703). This gives $\frac{4694 + 7410}{12703} = \frac{12104}{12703} \approx 0.953$.

Question 19

So far this season, the university's football team has executed 155 running plays, 143 passing plays, and 19 "trick" plays. What is the probability that the team will not execute
A trick play?

Accepted Answer

The probability of not executing a trick play is the number of non-trick plays divided by the total number of plays. There are 155 + 143 = 298 non-trick plays, and 155 + 143 + 19 = 317 total plays. So the probability of not executing a trick play is 298/317 = 0.94.

Question 20

A jar contains four white marbles, five red marbles, and six black marbles. If a marble were selected at random, the probability that it is white or black would be $\frac { 2 } { 3 }$.

Accepted Answer

The total number of marbles is 15 (4 white + 5 red + 6 black). The probability of selecting a white or black marble is the sum of their individual probabilities, which is $\frac{4}{15} + \frac{6}{15} = \frac{10}{15} = \frac{2}{3}$.

Quiz 4: Probability and Counting Rules

A coin is tossed 758 times and comes up heads 409 times. Use the Empirical Method to approximate the probability that the coin comes up heads.

The arrow on the spinner shown below can be spun so that the arrowhead eventually stops in one of the three sectors labeled "A", "B", or "C". The spinner is spun 124 times and comes up "A" 52 times. Use the Empirical Rule to approximate the probability that tl spinner comes up "A".

At a certain college, there were 700 science majors, 300 engineering majors, and business majors. If one student was selected at random, the probability that the student Is an engineering major is

At Wassamatta University, 59.3% of the student body are males. Choose one student at random. What is the probability that the student is female?

A Karate club consists of 41 persons holding a black belt (highest rating) , 59 persons holding a brown belt (middle rating) , and 73 persons holding a purple belt (lowest Rating) . What is the probability that a randomly-selected club member holds a brown belt Or a purple belt?

A Karate club consists of 52 persons holding a black belt (highest rating) , 69 persons holding a brown belt (middle rating) , and 83 persons holding a purple belt (lowest Rating) . What is the probability that a randomly-selected club member holds a black belt?

So far this season, the university's football team has executed 145 running plays, 149 passing plays, and 24 "trick" plays. What is the probability that the team will execute a Passing play?

The staff at a small company includes: 4 secretaries, 20 technicians, 4 engineers, 2 executives, and 50 factory workers. If a person is selected at random, what is the Probability that he or she is a factory worker?

So far this season, the university's football team has executed 155 running plays, 143 passing plays, and 19 "trick" plays. What is the probability that the team will not execute A trick play?

A jar contains four white marbles, five red marbles, and six black marbles. If a marble were selected at random, the probability that it is white or black would be $\frac { 2 } { 3 }$ .

Quiz 4: Probability and Counting Rules

A coin is tossed 758 times and comes up heads 409 times. Use the Empirical Method to approximate the probability that the coin comes up heads.

The arrow on the spinner shown below can be spun so that the arrowhead eventually stops in one of the three sectors labeled "A", "B", or "C". The spinner is spun 124 times and comes up "A" 52 times. Use the Empirical Rule to approximate the probability that tl spinner comes up "A".

At a certain college, there were 700 science majors, 300 engineering majors, and business majors. If one student was selected at random, the probability that the student Is an engineering major is

At Wassamatta University, 59.3% of the student body are males. Choose one student at random. What is the probability that the student is female?

Box A contains the numbers 1,2,31,2,31,2,3 , and 4 . Box B contains the numbers 5,6,75,6,75,6,7 , and 8.A18 . \mathrm { A } _ { 1 }8.A1​ first drawn from Box A and then another number from Box B. Using the figure below, ho outcomes are possible if both numbers are even? umber is

A Karate club consists of 41 persons holding a black belt (highest rating) , 59 persons holding a brown belt (middle rating) , and 73 persons holding a purple belt (lowest Rating) . What is the probability that a randomly-selected club member holds a brown belt Or a purple belt?

A Karate club consists of 52 persons holding a black belt (highest rating) , 69 persons holding a brown belt (middle rating) , and 83 persons holding a purple belt (lowest Rating) . What is the probability that a randomly-selected club member holds a black belt?

So far this season, the university's football team has executed 145 running plays, 149 passing plays, and 24 "trick" plays. What is the probability that the team will execute a Passing play?

The staff at a small company includes: 4 secretaries, 20 technicians, 4 engineers, 2 executives, and 50 factory workers. If a person is selected at random, what is the Probability that he or she is a factory worker?

So far this season, the university's football team has executed 155 running plays, 143 passing plays, and 19 "trick" plays. What is the probability that the team will not execute A trick play?

A jar contains four white marbles, five red marbles, and six black marbles. If a marble were selected at random, the probability that it is white or black would be 23\frac { 2 } { 3 }32​ .

A jar contains four white marbles, five red marbles, and six black marbles. If a marble were selected at random, the probability that it is white or black would be $\frac { 2 } { 3 }$ .