Question 1

Find the indicated probability.
-If two balanced dice are rolled, the possible outcomes can be represented as follows. $( 1,1 ) ( 2,1 ) ( 3,1 ) ( 4,1 ) ( 5,1 ) ( 6,1 )$
$( 1,2 ) ( 2,2 ) ( 3,2 ) ( 4,2 ) ( 5,2 ) ( 6,2 )$
$( 1,3 ) ( 2,3 ) ( 3,3 ) ( 4,3 ) ( 5,3 ) ( 6,3 )$
$( 1,4 ) ( 2,4 ) ( 3,4 ) ( 4,4 ) ( 5,4 ) ( 6,4 )$
$( 1,5 ) ( 2,5 ) ( 3,5 ) ( 4,5 ) ( 5,5 ) ( 6,5 )$
$( 1,1 ) ( 2,1 ) ( 3,1 ) ( 4,1 ) ( 5,1 ) ( 6,1 )$
$( 1,2 ) ( 2,2 ) ( 3,2 ) ( 4,2 ) ( 5,2 ) ( 6,2 )$
$( 1,3 ) ( 2,3 ) ( 3,3 ) ( 4,3 ) ( 5,3 ) ( 6,3 )$
$( 1,4 ) ( 2,4 ) ( 3,4 ) ( 4,4 ) ( 5,4 ) ( 6,4 )$
$( 1,5 ) ( 2,5 ) ( 3,5 ) ( 4,5 ) ( 5,5 ) ( 6,5 )$
$( 1,6 ) ( 2,6 ) ( 3,6 ) ( 4,6 ) ( 5,6 ) ( 6,6 )$

Determine the probability that the sum of the dice is $9 .$
A) $\frac { 5 } { 36 }$

B) $\frac { 1 } { 9 }$

C) $\frac { 1 } { 6 }$

D) $\frac { 1 } { 12 }$

Accepted Answer

The answer of Find the indicated probability.
-If two balanced dice...

Question 2

Suppose you randomly select a family with three children. Assume that births of boys and girls are equally likely. What is the probability that the family has at least one boy?
A)0.857
B)0.75
C)0.125
D)0.875

Accepted Answer

The probability of having at least one boy can be calculated by subtracting the probability of having no boys (all girls) from 1. Since each child can be a boy or a girl with equal probability, the probability of having three girls is (1/2)^3 = 1/8. Therefore, the probability of having at least one boy is 1 - 1/8 = 7/8 = 0.875.

Question 3

Find the indicated probability.
-On a multiple choice test, each question has 6 possible answers. If you make a random guess on the first question, what is the probability that you are correct?

A) 0
B) $\frac { 1 } { 6 }$
C) 1
D) 6

Accepted Answer

Since there are 6 possible answers and only one is correct, the probability of guessing the correct answer randomly is 1 out of 6, or $\frac{1}{6}$.

Question 4

In a poll, respondents were asked whether they had ever been in a car accident. 204 respondents indicated thatthey had been in a car accident and 365 respondents said that they had not been in a car accident. If one of these respondents is randomly selected, what is the probability of getting someone who has been in a car accident?
Round to the nearest thousandth, if necessary.
A)0.641
B)0.559
C)0.005
D)0.359

Accepted Answer

The probability is calculated by dividing the number of respondents who have been in a car accident by the total number of respondents. So, $ \frac{204}{204 + 365} = \frac{204}{569} \approx 0.359 $.

Question 5

Find the indicated probability.
-A bag contains four chips of which one is red, one is blue, one is green, and one is yellow. A chip is selected atrandom from the bag and then replaced in the bag. A second chip is then selected at random. Make a list of thepossible outcomes (for example RB represents the outcome red chip followed by blue chip)and use your list todetermine the probability that one blue chip and one green chip are selected. 
A) $\frac { 1 } { 4 }$

B) $\frac { 1 } { 2 }$

C) $\frac { 1 } { 16 }$

D) $\frac { 1 } { 8 }$

Accepted Answer

The possible outcomes for selecting one blue chip and one green chip are BG and GB. Since there are 4 options for the first draw and 4 for the second (because the chip is replaced), there are 16 possible outcomes in total. Thus, the probability is 2/16 = 1/8.

Question 6

Find the indicated probability.
-A bag contains 6 red marbles, 3 blue marbles, and 5 green marbles. If a marble is randomly selected from the bag, what is the probability that it is blue? 
A) $\frac { 1 } { 11 }$

B) $\frac { 1 } { 5 }$

C) $\frac { 3 } { 14 }$

D) $\frac { 1 } { 3 }$

Accepted Answer

The total number of marbles is 6 (red) + 3 (blue) + 5 (green) = 14. The probability of selecting a blue marble is the number of blue marbles (3) divided by the total number of marbles (14), which is $\frac{3}{14}$.

Question 7

A multiple choice Statistics exam has 10 possible answers for each question, only one of which is correct. If you guess randomly on every question, what score might you expect to get? Express your answer as a percentage.
A)90%
B)50%
C)15%
D)10%

Accepted Answer

Since there are 10 possible answers for each question and only one correct answer, the probability of guessing the correct answer randomly is 1/10 or 10%.

Question 8

Find the indicated probability.
-A die with 12 sides is rolled. What is the probability of rolling a number less than 11? 
A) 10
B) $\frac { 11 } { 12 }$

C) $\frac { 1 } { 12 }$

D) $\frac { 5 } { 6 }$

Accepted Answer

The answer of Find the indicated probability.
-A die with 12...

Question 9

Find the indicated probability.
-Two 6-sided dice are rolled. What is the probability that the sum of the two numbers on the dice will Be 3? 
A) $\frac { 1 } { 18 }$

B) $\frac { 17 } { 18 }$

C) $\frac { 1 } { 2 }$

D) 2

Accepted Answer

The sum of 3 can be achieved only by rolling a 1 on one die and a 2 on the other die. There are 2 ways this can happen (1 on the first die and 2 on the second, or 2 on the first die and 1 on the second) out of a total of 36 possible outcomes (6 sides on the first die times 6 sides on the second die), so the probability is $ \frac{2}{36} = \frac{1}{18} $.

Question 10

Find the indicated probability.
-If two balanced dice are rolled, the possible outcomes can be represented as follows. $( 1,1 ) ( 2,1 ) ( 3,1 ) ( 4,1 ) ( 5,1 ) ( 6,1 )$
$( 1,2 ) ( 2,2 ) ( 3,2 ) ( 4,2 ) ( 5,2 ) ( 6,2 )$
$( 1,3 ) ( 2,3 ) ( 3,3 ) ( 4,3 ) ( 5,3 ) ( 6,3 )$
$( 1,4 ) ( 2,4 ) ( 3,4 ) ( 4,4 ) ( 5,4 ) ( 6,4 )$
$( 1,5 ) ( 2,5 ) ( 3,5 ) ( 4,5 ) ( 5,5 ) ( 6,5 )$
$( 1,6 ) ( 2,6 ) ( 3,6 ) ( 4,6 ) ( 5,6 ) ( 6,6 )$
Determine the probability that the sum of the dice is 4 or 10 .
A) $\frac { 2 } { 9 }$

B) $\frac { 5 } { 36 }$

C) $\frac { 7 } { 36 }$

D) $\frac { 1 } { 6 }$

Accepted Answer

The answer of Find the indicated probability.
-If two balanced dice...

Question 11

Find the indicated probability.
-A committee of three people is to be formed. The three people will be selected from a list of five possible committee members. A simple random sample of three people is taken, without replacement, from the group of five people. Using the letters A, B, C, D, E to represent the five people, list the possible samples of size three and use your list to determine the probability that B is included in the sample. (Hint: There are 10 possible samples.) 
A) $\frac { 1 } { 2 }$

B) $\frac { 2 } { 5 }$

C) $\frac { 3 } { 5 }$

D) $\frac { 7 } { 10 }$

Accepted Answer

The answer of Find the indicated probability.
-A committee of three...

Question 12

Find the indicated probability.
-A bag contains four chips of which one is red, one is blue, one is green, and one is yellow. A chip is selected at random from the bag and then replaced in the bag. A second chip is then selected at random. Make a list of the possible outcomes (for example RB represents the outcome red chip followed by blue chip)and use your list to determine the probability that the two chips selected are different colors.
(Hint: There are 16 possible outcomes.) 
A) $\frac { 3 } { 8 }$

B) $\frac { 3 } { 4 }$

C) $\frac { 1 } { 2 }$

D) $\frac { 3 } { 16 }$

Accepted Answer

Since there are 16 possible outcomes and 12 of these involve selecting chips of different colors (each color can be followed by a chip of any of the three other colors, making 4*3=12 outcomes), the probability is $\frac{12}{16} = \frac{3}{4}$.

Question 13

Find the indicated probability.
-If a person is randomly selected, find the probability that his or her birthday is in December. Ignore leap years. 
A) $\frac { 1 } { 31 }$

B) $\frac { 1 } { 365 }$

C) $\frac { 31 } { 365 }$

D) $\frac { 1 } { 12 }$

Accepted Answer

December has 31 days out of the 365 days in a non-leap year, so the probability that a randomly selected person has a birthday in December is $\frac{31}{365}$.

Question 14

Find the indicated probability.
-Sammy and Sally each carry a bag containing a banana, a chocolate bar, and a licorice stick. Simultaneously, they take out a single food item and consume it. The possible pairs of food items that Sally and Sammy consumed are as follows.

chocolate bar - chocolate bar
licorice stick - chocolate bar
banana - banana
chocolate bar - licorice stick
licorice stick - licorice stick
chocolate bar - banana
banana - licorice stick
licorice stick - banana
banana - chocolate bar

Find the probability that at least one banana was eaten. 
A) $\frac { 4 } { 5 }$

B) $\frac { 5 } { 9 }$

C) $\frac { 7 } { 9 }$

D) $\frac { 1 } { 3 }$

Accepted Answer

The answer of Find the indicated probability.
-Sammy and Sally each...

Question 15

Determine the probability of the given opposite event.
-If $\mathrm { P } ( \mathrm { A } ) = \frac { 6 } { 11 }$, find $\mathrm { P } ( \overline { \mathrm { A } } )$.

A) $\frac { 6 } { 17 }$

B) $\frac { 11 } { 6 }$

C) $\frac { 5 } { 11 }$

D) 0

Accepted Answer

The probability of the opposite event, denoted as $\mathrm { P } ( \overline { \mathrm { A } } )$, is found by subtracting the given probability from 1: $1 - \frac { 6 } { 11 } = \frac { 5 } { 11 }$.

Question 16

Find the indicated probability.
-If you flip a coin three times, the possible outcomes are HHH, HHT, HTH, HTT, THH, THT, TTH, TTT. What is the probability of getting at least one head? 
A) $\frac { 7 } { 8 }$

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

C) $\frac { 1 } { 2 }$

D) $\frac { 3 } { 4 }$

Accepted Answer

The probability of getting at least one head is found by subtracting the probability of getting no heads (TTT) from 1. Since there is only one way to get no heads out of 8 possible outcomes, the probability is $1 - \frac{1}{8} = \frac{7}{8}$.

Question 17

Find the indicated probability.
-If you flip a coin three times, the possible outcomes are HHH, HHT, HTH, HTT, THH, THT, TTH, TTT. What isthe probability of getting at least two heads? 
A) $\frac { 1 } { 8 }$

B) $\frac { 5 } { 8 }$

C) $\frac { 1 } { 2 }$

D) $\frac { 3 } { 8 }$

Accepted Answer

The answer of Find the indicated probability.
-If you flip a...

Question 18

Find the indicated probability.
-A class consists of 41 women and 37 men. If a student is randomly selected, what is the probability that the
Student is a woman? 
A) $\frac { 41 } { 78 }$

B) $\frac { 41 } { 37 }$

C) $\frac { 1 } { 78 }$

D) $\frac { 37 } { 78 }$

Accepted Answer

The total number of students is 41 women + 37 men = 78 students. The probability of selecting a woman is the number of women divided by the total number of students, which is $\frac{41}{78}$.

Question 19

Find the indicated probability.
-A committee of three people is to be formed. The three people will be selected from a list of five possible committeemembers. A simple random sample of three people is taken, without replacement, from the group of five people. If thefive people are represented by the letters A, B, C, D, E, the possible outcomes are as follows. 
$\begin{array}{l}
\mathrm{ABC} \
\mathrm{ABD} \
\mathrm{ABE} \
\mathrm{ACD} \
\mathrm{ACE} \
\mathrm{ADE} \
\mathrm{BCD} \
\mathrm{BCE} \
\mathrm{BDE}
\end{array}$

Determine the probability that B and C are both included in the sample. 
A) $\frac { 3 } { 10 }$

B) $\frac { 1 } { 10 }$

C) $\frac { 9 } { 10 }$

D) $\frac { 2 } { 10 }$

Accepted Answer

The probability that B and C are both included in the sample is calculated by counting the number of outcomes that include both B and C and dividing by the total number of outcomes. There are 3 outcomes (BCD, BCE, BDE) that include both B and C out of a total of 10 possible outcomes, so the probability is $\frac{3}{10}$.

Question 20

Find the indicated probability.
-If you flip a coin three times, the possible outcomes are HHH, HHT, HTH, HTT, THH, THT, TTH, TTT. What is the probability that the first two tosses come up the same? 
A) $\frac { 3 } { 8 }$

B) $\frac { 1 } { 8 }$

C) $\frac { 1 } { 2 }$

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

Accepted Answer

The first two tosses can either be HH or TT, which are 2 out of the 4 possible outcomes for the first two flips (HH, HT, TH, TT), making the probability $\frac{2}{4} = \frac{1}{2}$.

Quiz 6: Probability in Statistics

Suppose you randomly select a family with three children. Assume that births of boys and girls are equally likely. What is the probability that the family has at least one boy?

Find the indicated probability. -On a multiple choice test, each question has 6 possible answers. If you make a random guess on the first question, what is the probability that you are correct?

Find the indicated probability. -A bag contains 6 red marbles, 3 blue marbles, and 5 green marbles. If a marble is randomly selected from the bag, what is the probability that it is blue?

A multiple choice Statistics exam has 10 possible answers for each question, only one of which is correct. If you guess randomly on every question, what score might you expect to get? Express your answer as a percentage.

Find the indicated probability. -A die with 12 sides is rolled. What is the probability of rolling a number less than 11?

Find the indicated probability. -Two 6-sided dice are rolled. What is the probability that the sum of the two numbers on the dice will Be 3?

Find the indicated probability. -If a person is randomly selected, find the probability that his or her birthday is in December. Ignore leap years.

Determine the probability of the given opposite event. -If $\mathrm { P } ( \mathrm { A } ) = \frac { 6 } { 11 }$ , find $\mathrm { P } ( \overline { \mathrm { A } } )$ .

Find the indicated probability. -If you flip a coin three times, the possible outcomes are HHH, HHT, HTH, HTT, THH, THT, TTH, TTT. What is the probability of getting at least one head?

Find the indicated probability. -If you flip a coin three times, the possible outcomes are HHH, HHT, HTH, HTT, THH, THT, TTH, TTT. What isthe probability of getting at least two heads?

Find the indicated probability. -A class consists of 41 women and 37 men. If a student is randomly selected, what is the probability that the Student is a woman?

Find the indicated probability. -If you flip a coin three times, the possible outcomes are HHH, HHT, HTH, HTT, THH, THT, TTH, TTT. What is the probability that the first two tosses come up the same?

Quiz 6: Probability in Statistics

Suppose you randomly select a family with three children. Assume that births of boys and girls are equally likely. What is the probability that the family has at least one boy?

Find the indicated probability. -On a multiple choice test, each question has 6 possible answers. If you make a random guess on the first question, what is the probability that you are correct?

Find the indicated probability. -A bag contains 6 red marbles, 3 blue marbles, and 5 green marbles. If a marble is randomly selected from the bag, what is the probability that it is blue?

A multiple choice Statistics exam has 10 possible answers for each question, only one of which is correct. If you guess randomly on every question, what score might you expect to get? Express your answer as a percentage.

Find the indicated probability. -A die with 12 sides is rolled. What is the probability of rolling a number less than 11?

Find the indicated probability. -Two 6-sided dice are rolled. What is the probability that the sum of the two numbers on the dice will Be 3?

Find the indicated probability. -If a person is randomly selected, find the probability that his or her birthday is in December. Ignore leap years.

Determine the probability of the given opposite event. -If P(A) =611\mathrm { P } ( \mathrm { A } ) = \frac { 6 } { 11 }P(A) =116​ , find P(A‾) \mathrm { P } ( \overline { \mathrm { A } } ) P(A) .

Find the indicated probability. -If you flip a coin three times, the possible outcomes are HHH, HHT, HTH, HTT, THH, THT, TTH, TTT. What is the probability of getting at least one head?

Find the indicated probability. -If you flip a coin three times, the possible outcomes are HHH, HHT, HTH, HTT, THH, THT, TTH, TTT. What isthe probability of getting at least two heads?

Find the indicated probability. -A class consists of 41 women and 37 men. If a student is randomly selected, what is the probability that the Student is a woman?

Find the indicated probability. -If you flip a coin three times, the possible outcomes are HHH, HHT, HTH, HTT, THH, THT, TTH, TTT. What is the probability that the first two tosses come up the same?

Determine the probability of the given opposite event. -If $\mathrm { P } ( \mathrm { A } ) = \frac { 6 } { 11 }$ , find $\mathrm { P } ( \overline { \mathrm { A } } )$ .