Question 1

Construct the requested tree diagram.
-Use the tree diagram to count how many four-child families have two boys and two girls.

Accepted Answer

A)  2 families 
B)  6 families 
C)  4 families 
D)  8 families 
A)  2 families 
B)  6 families 
C)  4 families 
D)  8 families

Question 2

Find the probability.
-Two dice are rolled. Find the probability that the score on the dice is either 8 or at most 3.

Accepted Answer

A)  $\frac { 11 } { 36 }$ 
B)  $\frac { 7 } { 36 }$ 
C)  $\frac { 1 } { 4 }$ 
D)  $\frac { 2 } { 9 }$ 
A)  $\frac { 11 } { 36 }$ 
B)  $\frac { 7 } { 36 }$ 
C)  $\frac { 1 } { 4 }$ 
D)  $\frac { 2 } { 9 }$

Question 3

Solve the problem.
-A calculator requires a keystroke assembly and a logic circuit. Assume that 88% of the keystroke assemblies and 86% of the logic circuits are satisfactory. Find the probability that a finished Calculator will be satisfactory.

Accepted Answer

A) 0.8700 
B) 0.7744 
C) 0.7396 
D) 0.7568 
A) 0.8700 
B) 0.7744 
C) 0.7396 
D) 0.7568

Question 4

Determine whether the players have equal probabilities of winning.
-Draw two cards from a regular deck. If cards of the same suit are drawn, player 1 wins; if cards of the same color are drawn, player 2 wins.

Accepted Answer

A) Yes 
B) No 
A) Yes 
B) No

Question 5

Find the probability.
-A bag contains 9 red marbles, 5 blue marbles, and 2 green marbles. What is the probability of choosing a blue marble?

Accepted Answer

A)  $\frac { 5 } { 16 }$ 
B)  $\frac { 1 } { 8 }$ 
C)  $\frac { 5 } { 14 }$ 
D)  $\frac { 9 } { 16 }$ 
A)  $\frac { 5 } { 16 }$ 
B)  $\frac { 1 } { 8 }$ 
C)  $\frac { 5 } { 14 }$ 
D)  $\frac { 9 } { 16 }$

Question 6

Determine whether the players have equal probabilities of winning.
-Toss two fair dice numbered 1 through 6. If the sum is 3, player 1 wins; if the sum is 12, player 2 wins.

Accepted Answer

A) Yes 
B) No 
A) Yes 
B) No

Question 7

Find the probability.
-If you are dealt two cards successively (without replacement)from a standard 52-card deck, find the probability of getting two black cards.

Accepted Answer

A)  $\frac { 1 } { 2,652 }$ 
B)  $\frac { 25 } { 102 }$ 
C)  $\frac { 13 } { 51 }$ 
D)  $\frac { 25 } { 51 }$ 
A)  $\frac { 1 } { 2,652 }$ 
B)  $\frac { 25 } { 102 }$ 
C)  $\frac { 13 } { 51 }$ 
D)  $\frac { 25 } { 51 }$

Question 8

Solve the problem.
-What is the probability that the arrow will land on an odd number?

Accepted Answer

A)  1 
B)  $\frac { 3 } { 5 }$ 
C)  0 
D)  $\frac { 2 } { 5 }$ 
A)  1 
B)  $\frac { 3 } { 5 }$ 
C)  0 
D)  $\frac { 2 } { 5 }$

Question 9

Construct the requested tree diagram.
-Construct a tree diagram that shows all possible 2 -letter code words using only the letters  x  and  y  with repetition allowed.

Accepted Answer

A)    
B)   
C)    
D)    
A)    
B)   
C)    
D)

Question 10

Determine the number of outcomes as requested.
-Two 6-sided dice are thrown. Determine the number of ways that a score which is a multiple of 3 can be obtained.

Accepted Answer

A) 11 
B) 2 
C) 6 
D) 12 
A) 11 
B) 2 
C) 6 
D) 12

Question 11

Solve the problem.
-Suppose there is a 0.009 chance the main computer will fail in a given time period and a 0.012 chance the backup computer will fail while the main computer is being repaired. Assume that the Failures are independent. Find the probability of both computers being down.

Accepted Answer

A) 0.00014 
B) 0.00011 
C) 0.00008 
D) 0.00108 
A) 0.00014 
B) 0.00011 
C) 0.00008 
D) 0.00108

Question 12

Solve the problem.
-At a track meet with 135 participants, 25 participate in jumping events,  $\frac { 1 } { 5 }$ of these jumpers are female, and $\frac { 1 } { 3 }$ of the total participants are female. What is the probability that a participant chosen at random is a jumper, given that the person is a female?

Accepted Answer

A)  $\frac { 1 } { 15 }$ 
B)  $\frac { 1 } { 675 }$ 
C)  $\frac { 5 } { 27 }$ 
D)  $\frac { 1 } { 9 }$ 
A)  $\frac { 1 } { 15 }$ 
B)  $\frac { 1 } { 675 }$ 
C)  $\frac { 5 } { 27 }$ 
D)  $\frac { 1 } { 9 }$

Question 13

Determine whether the players have equal probabilities of winning.
-Draw a card from a regular deck. If a club is drawn, player 1 wins; if a diamond is drawn, player 2 wins.

Accepted Answer

A) Yes 
B) No 
A) Yes 
B) No

Question 14

Construct the requested tree diagram.
-Three coins are tossed. Use the tree diagram to count how many ways the outcome consists of two heads and one tail.

Accepted Answer

A)  3 outcomes 
B)  6 outcomes 
C)  4 outcomes 
D)  2 outcomes 
A)  3 outcomes 
B)  6 outcomes 
C)  4 outcomes 
D)  2 outcomes

Question 15

Find the probability.
-One digit from the number 3,474,554 is written on each of seven cards. What is the probability of drawing a card that shows 5?

Accepted Answer

A)  1 
B)  $\frac { 2 } { 7 }$ 
C)  $\frac { 5 } { 7 }$ 
D)  $\frac { 1 } { 7 }$ 
A)  1 
B)  $\frac { 2 } { 7 }$ 
C)  $\frac { 5 } { 7 }$ 
D)  $\frac { 1 } { 7 }$

Question 16

Find the probability.
-Two dice are rolled. Find the probability that the score on the dice is 11.

Accepted Answer

A)  $\frac { 1 } { 18 }$ 
B)  $\frac { 1 } { 3 }$ 
C)  $\frac { 5 } { 18 }$ 
D)  $\frac { 11 } { 36 }$ 
A)  $\frac { 1 } { 18 }$ 
B)  $\frac { 1 } { 3 }$ 
C)  $\frac { 5 } { 18 }$ 
D)  $\frac { 11 } { 36 }$

Question 17

Solve the problem.
-A husband and wife have a $\frac { 1 } { 3 }$ probability of passing on brown eyes to their children. If they have four children, what is the probability of none of the children having brown eyes?

Accepted Answer

A)  $\frac { 1 } { 27 }$ 
B)  $\frac { 1 } { 81 }$ 
C)  $\frac { 4 } { 81 }$ 
D)  $\frac { 1 } { 7 }$ 
A)  $\frac { 1 } { 27 }$ 
B)  $\frac { 1 } { 81 }$ 
C)  $\frac { 4 } { 81 }$ 
D)  $\frac { 1 } { 7 }$

Question 18

Two marbles are drawn without replacement from a box with 3 white, 2 green, 2 red, and 1 blue marble. Find the probability.
-The first marble is blue and the second marble is white.

Accepted Answer

A)  $\frac { 3 } { 64 }$ 
B)  $\frac { 3 } { 7 }$ 
C)  $\frac { 2 } { 7 }$ 
D)  $\frac { 3 } { 56 }$ 
A)  $\frac { 3 } { 64 }$ 
B)  $\frac { 3 } { 7 }$ 
C)  $\frac { 2 } { 7 }$ 
D)  $\frac { 3 } { 56 }$

Question 19

Solve the problem.
-The following list of digits was taken from a table of random numbers. We will let them represent 50 tosses of 5 fair coins. If a digit is 0 - 4, it will be an H, and the digit 5 - 9 will be a T. Use this Simulation to estimate the probability of getting two heads on a toss of five coins. $\begin{array}{lllll}
18728 & 94741 & 32063 & 04963 & 54859 \
15592 & 71357 & 28152 & 11732 & 17173 \
89555 & 75520 & 08882 & 95295 & 72895 \
38894 & 58070 & 77371 & 10194 & 94917 \
64336 & 95103 & 90740 & 03577 & 62599
\end{array}$

$\begin{array}{lllll}
52052 & 24004 & 03845 & 11507 & 45233 \
27510 & 33761 & 86563 & 61729 & 39087 \
48061 & 59412 & 79969 & 11339 & 27067 \
27324 & 72723 & 22406 & 86253 & 26409 \
29970 & 95877 & 70975 & 99129 & 16866
\end{array}$

Accepted Answer

A)  $\frac { 1 } { 4 }$ 
B)  $\frac { 6 } { 25 }$ 
C)  $\frac { 1 } { 2 }$ 
D)  $\frac { 8 } { 25 }$ 
A)  $\frac { 1 } { 4 }$ 
B)  $\frac { 6 } { 25 }$ 
C)  $\frac { 1 } { 2 }$ 
D)  $\frac { 8 } { 25 }$

Question 20

Solve the problem.
-A bag contains 15 balls numbered 1 through 15. What are the odds in favor of selecting a ball that has an even number?

Accepted Answer

A) 7 : 8 
B) 15 : -8 
C) 7 : 15 
D) 2 : 13 
A) 7 : 8 
B) 15 : -8 
C) 7 : 15 
D) 2 : 13

Construct the requested tree diagram. -Use the tree diagram to count how many four-child families have two boys and two girls.

Find the probability. -Two dice are rolled. Find the probability that the score on the dice is either 8 or at most 3.

Solve the problem. -A calculator requires a keystroke assembly and a logic circuit. Assume that 88% of the keystroke assemblies and 86% of the logic circuits are satisfactory. Find the probability that a finished Calculator will be satisfactory.

Determine whether the players have equal probabilities of winning. -Draw two cards from a regular deck. If cards of the same suit are drawn, player 1 wins; if cards of the same color are drawn, player 2 wins.

Find the probability. -A bag contains 9 red marbles, 5 blue marbles, and 2 green marbles. What is the probability of choosing a blue marble?

Determine whether the players have equal probabilities of winning. -Toss two fair dice numbered 1 through 6. If the sum is 3, player 1 wins; if the sum is 12, player 2 wins.

Find the probability. -If you are dealt two cards successively (without replacement)from a standard 52-card deck, find the probability of getting two black cards.

Solve the problem. -What is the probability that the arrow will land on an odd number?

Construct the requested tree diagram. -Construct a tree diagram that shows all possible 2 -letter code words using only the letters x and y with repetition allowed.

Determine the number of outcomes as requested. -Two 6-sided dice are thrown. Determine the number of ways that a score which is a multiple of 3 can be obtained.

Solve the problem. -Suppose there is a 0.009 chance the main computer will fail in a given time period and a 0.012 chance the backup computer will fail while the main computer is being repaired. Assume that the Failures are independent. Find the probability of both computers being down.

Determine whether the players have equal probabilities of winning. -Draw a card from a regular deck. If a club is drawn, player 1 wins; if a diamond is drawn, player 2 wins.

Construct the requested tree diagram. -Three coins are tossed. Use the tree diagram to count how many ways the outcome consists of two heads and one tail.

Find the probability. -One digit from the number 3,474,554 is written on each of seven cards. What is the probability of drawing a card that shows 5?

Find the probability. -Two dice are rolled. Find the probability that the score on the dice is 11.

Solve the problem. -A husband and wife have a $\frac { 1 } { 3 }$ probability of passing on brown eyes to their children. If they have four children, what is the probability of none of the children having brown eyes?

Two marbles are drawn without replacement from a box with 3 white, 2 green, 2 red, and 1 blue marble. Find the probability. -The first marble is blue and the second marble is white.

Solve the problem. -A bag contains 15 balls numbered 1 through 15. What are the odds in favor of selecting a ball that has an even number?

An Introduction to Problem Solving

Introduction to Logic and Sets

Numeration Systems and Whole Number Operations

Number Theory

Integers

Rational Numbers and Proportional Reasoning

Rational Numbers As Decimals and Percents

Real Numbers and Algebraic Thinking

Data Analysisstatistics: an Introduction

Introductory Geometry

Congruence and Similarity With Constructions

Congruence and Similarity With Transformations

Area, Pythagorean Theorem, and Volume

Filters

Exam 9: Probability

Construct the requested tree diagram. -Use the tree diagram to count how many four-child families have two boys and two girls.

Find the probability. -Two dice are rolled. Find the probability that the score on the dice is either 8 or at most 3.

Solve the problem. -A calculator requires a keystroke assembly and a logic circuit. Assume that 88% of the keystroke assemblies and 86% of the logic circuits are satisfactory. Find the probability that a finished Calculator will be satisfactory.

Determine whether the players have equal probabilities of winning. -Draw two cards from a regular deck. If cards of the same suit are drawn, player 1 wins; if cards of the same color are drawn, player 2 wins.

Find the probability. -A bag contains 9 red marbles, 5 blue marbles, and 2 green marbles. What is the probability of choosing a blue marble?

Determine whether the players have equal probabilities of winning. -Toss two fair dice numbered 1 through 6. If the sum is 3, player 1 wins; if the sum is 12, player 2 wins.

Find the probability. -If you are dealt two cards successively (without replacement)from a standard 52-card deck, find the probability of getting two black cards.

Solve the problem. -What is the probability that the arrow will land on an odd number?

Construct the requested tree diagram. -Construct a tree diagram that shows all possible 2 -letter code words using only the letters x and y with repetition allowed.

Determine the number of outcomes as requested. -Two 6-sided dice are thrown. Determine the number of ways that a score which is a multiple of 3 can be obtained.

Solve the problem. -Suppose there is a 0.009 chance the main computer will fail in a given time period and a 0.012 chance the backup computer will fail while the main computer is being repaired. Assume that the Failures are independent. Find the probability of both computers being down.

Determine whether the players have equal probabilities of winning. -Draw a card from a regular deck. If a club is drawn, player 1 wins; if a diamond is drawn, player 2 wins.

Construct the requested tree diagram. -Three coins are tossed. Use the tree diagram to count how many ways the outcome consists of two heads and one tail.

Find the probability. -One digit from the number 3,474,554 is written on each of seven cards. What is the probability of drawing a card that shows 5?

Find the probability. -Two dice are rolled. Find the probability that the score on the dice is 11.

Solve the problem. -A husband and wife have a 13\frac { 1 } { 3 }31​ probability of passing on brown eyes to their children. If they have four children, what is the probability of none of the children having brown eyes?

Two marbles are drawn without replacement from a box with 3 white, 2 green, 2 red, and 1 blue marble. Find the probability. -The first marble is blue and the second marble is white.

Solve the problem. -A bag contains 15 balls numbered 1 through 15. What are the odds in favor of selecting a ball that has an even number?

An Introduction to Problem Solving

Introduction to Logic and Sets

Numeration Systems and Whole Number Operations

Number Theory

Integers

Rational Numbers and Proportional Reasoning

Rational Numbers As Decimals and Percents

Real Numbers and Algebraic Thinking

Data Analysisstatistics: an Introduction

Introductory Geometry

Congruence and Similarity With Constructions

Congruence and Similarity With Transformations

Area, Pythagorean Theorem, and Volume

Filters

Solve the problem. -A husband and wife have a $\frac { 1 } { 3 }$ probability of passing on brown eyes to their children. If they have four children, what is the probability of none of the children having brown eyes?