Question 1

Solve the problem.
-The table below shows the results of a consumer survey of annual incomes in 100 households. $$\begin{array} { l | c } 
\text { Income } & \text { Number of households } \
\hline \$ 0 - 14,999 & 9 \
\hline \$ 15,000 - 24,999 & 25 \
\hline \$ 25,000 - 34,999 & 27 \
\hline \$ 35,000 - 44,999 & 25 \
\hline \$ 45,000 \text { or more } & 14
\end{array}$$ What is the probability that a household has an annual income between $15,000 and $44,999 inclusive?

Accepted Answer

A)  0.52 
B)  0.5 
C)  0.77 
D)  0.27

Question 2

Solve the problem.
-A spinner has regions numbered 1 through 21. What is the probability that the spinner will stop on an even number or a multiple of 3? A) $\frac { 10 } { 9 }$

Accepted Answer

B)  17 
C)  $\frac { 2 } { 3 }$ 
D)  $\frac { 1 } { 3 }$

Question 3

Solve the problem.
-A coin is weighted so that heads is 16 times as likely as tails to occur. What probability should be assigned to
heads? to tails?

Accepted Answer

The answer of Solve the problem.
-A coin is weighted so...

Question 4

Solve the problem.
-A certain mathematics test consists of 20 questions. Goldie decides to answer the questions without reading them. In how many ways can Goldie fill in the answer sheet if the possible answers are true and false?

Accepted Answer

A)  1,048,576 
B)  400 
C)  190 
D)  40

Question 5

Solve the problem.
-How many ways are there to choose a soccer team consisting of 3 forwards, 4 midfield players, and 3 defensive players, if the players are chosen from 6 forwards, 7 midfield players, and 5 defensive players?

Accepted Answer

A)  6,048,000 
B)  7,000 
C)  65 
D)  43,758

Question 6

Solve the problem.
-A man has 10 shirts and 9 ties. How many different shirt and tie arrangements can he wear?

Accepted Answer

A)  180 
B)  90 
C)  100 
D)  81

Question 7

Solve the problem.
-A survey of 2,504 credit card users indicated that 1,167 had bought books online, 1,226 had bought music online, 431 had bought pet supplies online, 128 had bought both books and music, 227 had bought both books and pet
Supplies, 198 had bought both music and pet supplies, and 99 had bought all three. How many credit card users
Did not buy any of the three? How many bought either books or pet supplies but not music?

Accepted Answer

A)  233; 1,016 
B)  134; 1,115 
C)  134; 1,144 
D)  134; 1,016

Question 8

Solve the problem.
-In a probability model, which of the following numbers could be the probability of an outcome: $0,0.2 , - 0.01 , - \frac { 1 } { 3 } , \frac { 1 } { 2 } , \frac { 5 } { 4 } , 1,1.5$

Accepted Answer

A)  $0,0.2 , - 0.01,1,1.5$ 
B)  $0,0.2 , \frac { 1 } { 2 } , 1$ 
C)  $0,0.2 , - 0.01 , - \frac { 1 } { 3 } , \frac { 1 } { 2 } , 1$ 
D)  $0.2 , \frac { 1 } { 2 } , 1$

Question 9

Solve the problem.
-A bag contains 9 red marbles, 3 blue marbles, and 7 green marbles. If one marble is selected at random, determine the probability that it is blue. A) $\frac { 3 } { 19 }$

Accepted Answer

B)  $\frac { 1 } { 4 }$ 
C)  $\frac { 9 } { 19 }$ 
D)  $\frac { 7 } { 19 }$

Question 10

Solve the problem.
-$$\begin{array} { l | r } 
\text { Outcome } & \text { Probability } \
\hline \text { Red } & - 0.21 \
\text { Blue } & 0.27 \
\text { Green } & 0.30 \
\text { White } & 0.22
\end{array}$$

Accepted Answer

A)  Yes 
B)  No

Question 11

Solve the problem.
-Find the probability of getting 2 tails when 3 fair coins are tossed. A) $\frac { 2 } { 3 }$

Accepted Answer

B)  $\frac { 1 } { 2 }$ 
C)  $\frac { 1 } { 4 }$ 
D)  $\frac { 3 } { 8 }$

Question 12

Solve the problem.
-Mary finds 8 fish at a pet store that she would like to buy, but she can afford only 5 of them. In how many ways can she make her selection? How many ways can she make her selection if he decides that one of the fish is a
Must?

Accepted Answer

A)  336; 210 
B)  3,360; 420 
C)  6,720; 840 
D)  56; 35

Question 13

Solve the problem.
-A twelve-sided die is weighted so that only the numbers 1 through 8 will appear and they will occur with the
same probability. What probability should be assigned to each face?

Accepted Answer

The answer of Solve the problem.
-A twelve-sided die is weighted...

Question 14

Solve the problem.
-Lisa has 4 skirts, 10 blouses, and 4 jackets. How many 3-piece outfits can she put together assuming any piece goes with any other?

Accepted Answer

A)  320 possible outfits 
B)  18 possible outfits 
C)  160 possible outfits 
D)  40 possible outfits

Question 15

Solve the problem.
-How many different 11-letter words (real or imaginary) can be formed from the letters of the word
MISSISSIPPI? Leave your answer in factorial form.

Accepted Answer

The answer of Solve the problem.
-How many different 11-letter words...

Question 16

Solve the problem.
-$$\begin{array} { l | c } 
\text { Outcome } & \text { Probability } \
\hline \text { Golfing } & 0.13 \
\text { Skiing } & 0.21 \
\text { Swimming } & 0.12 \
\text { Biking } & 0.28 \
\text { Hiking } & 0.26
\end{array}$$

Accepted Answer

A)  Yes 
B)  No

Question 17

Solve the problem.
-Given that P(A) = 0.14 and P(B) = 0.46, find P(A $P ( A \cap B )$

Accepted Answer

A)  0 
B)  0.27 
B)  if A and B are mutually exclusive. 
C)  0.253 
D)  0.0644

Question 18

onstruct a probability model for the experiment.
-Rolling a 6-sided fair die once

Accepted Answer

The answer of onstruct a probability model for the experiment.
-Rolling...

Question 19

Solve the problem.
-How many 2-letter codes can be formed using the letters A, B, C, D, E, F, G, H, and I. Repeated letters are allowed.

Accepted Answer

A)  36 
B)  72 
C)  512 
D)  81

Question 20

Find the value of the permutation.
-P(11, 4)

Accepted Answer

A)  1,663,200 
B)  10,080 
C)  7,920 
D)  3,960

Exam 12: Counting and Probability

Solve the problem. -A coin is weighted so that heads is 16 times as likely as tails to occur. What probability should be assigned to heads? to tails?

Solve the problem. -A certain mathematics test consists of 20 questions. Goldie decides to answer the questions without reading them. In how many ways can Goldie fill in the answer sheet if the possible answers are true and false?

Solve the problem. -How many ways are there to choose a soccer team consisting of 3 forwards, 4 midfield players, and 3 defensive players, if the players are chosen from 6 forwards, 7 midfield players, and 5 defensive players?

Solve the problem. -A man has 10 shirts and 9 ties. How many different shirt and tie arrangements can he wear?

Solve the problem. -In a probability model, which of the following numbers could be the probability of an outcome: $0,0.2 , - 0.01 , - \frac { 1 } { 3 } , \frac { 1 } { 2 } , \frac { 5 } { 4 } , 1,1.5$

Solve the problem. - $\begin{array} { l | r } \text { Outcome } & \text { Probability } \\\hline \text { Red } & - 0.21 \\\text { Blue } & 0.27 \\\text { Green } & 0.30 \\\text { White } & 0.22\end{array}$

Solve the problem. -Mary finds 8 fish at a pet store that she would like to buy, but she can afford only 5 of them. In how many ways can she make her selection? How many ways can she make her selection if he decides that one of the fish is a Must?

Solve the problem. -A twelve-sided die is weighted so that only the numbers 1 through 8 will appear and they will occur with the same probability. What probability should be assigned to each face?

Solve the problem. -Lisa has 4 skirts, 10 blouses, and 4 jackets. How many 3-piece outfits can she put together assuming any piece goes with any other?

Solve the problem. -How many different 11-letter words (real or imaginary) can be formed from the letters of the word MISSISSIPPI? Leave your answer in factorial form.

Solve the problem. - $\begin{array} { l | c } \text { Outcome } & \text { Probability } \\\hline \text { Golfing } & 0.13 \\\text { Skiing } & 0.21 \\\text { Swimming } & 0.12 \\\text { Biking } & 0.28 \\\text { Hiking } & 0.26\end{array}$

Solve the problem. -Given that P(A) = 0.14 and P(B) = 0.46, find P(A $P ( A \cap B )$

onstruct a probability model for the experiment. -Rolling a 6-sided fair die once

Solve the problem. -How many 2-letter codes can be formed using the letters A, B, C, D, E, F, G, H, and I. Repeated letters are allowed.

Find the value of the permutation. -P(11, 4)