Question 1

Solve the problem.
-Assume that the probability is $\frac { 1 } { 2 }$ that a child born is a boy. What is the probability that both of a family's two children are girls?

Accepted Answer

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

Question 2

Solve the problem.
-What is the probability of a dart landing in the shaded region? (Assume that the x's represent equal measures and that the dart is equally likely to land in any region on The board.)

Accepted Answer

A)  $\frac { 1 } { 2 }$ 
B)  $\frac { 3 } { 8 }$ 
C)  $\frac { 5 } { 8 }$ 
D)  $\frac { 3 } { 4 }$ 
A)  $\frac { 1 } { 2 }$ 
B)  $\frac { 3 } { 8 }$ 
C)  $\frac { 5 } { 8 }$ 
D)  $\frac { 3 } { 4 }$ B

Question 3

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

Accepted Answer

A)  $\frac { 3 } { 56 }$ 
B)  $\frac { 1 } { 16 }$ 
C)  $\frac { 1 } { 14 }$ 
D)  $\frac { 1 } { 28 }$ 
A)  $\frac { 3 } { 56 }$ 
B)  $\frac { 1 } { 16 }$ 
C)  $\frac { 1 } { 14 }$ 
D)  $\frac { 1 } { 28 }$ D

Question 4

Solve the problem.
-The following string of B's and G's was obtained from tossing a quarter 40 times. Heads were listed as  B  and tails as  G . Use this simulation to estimate the probability of two girls being born in succession.
$\{ \text { BBGGGGGBGGBBGGGBGGBBBGBBGBBBBGGBBGGBGGBG } \}$

Accepted Answer

A)  $\frac { 10 } { 40 }$ 
B)  $\frac { 10 } { 39 }$ 
C)  $\frac { 11 } { 40 }$ 
D)  $\frac { 11 } { 39 }$ 
A)  $\frac { 10 } { 40 }$ 
B)  $\frac { 10 } { 39 }$ 
C)  $\frac { 11 } { 40 }$ 
D)  $\frac { 11 } { 39 }$

Question 5

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 red.

Accepted Answer

A)  $\frac { 2 } { 7 }$ 
B)  $\frac { 1 } { 56 }$ 
C)  $\frac { 1 } { 7 }$ 
D)  $\frac { 1 } { 28 }$ 
A)  $\frac { 2 } { 7 }$ 
B)  $\frac { 1 } { 56 }$ 
C)  $\frac { 1 } { 7 }$ 
D)  $\frac { 1 } { 28 }$

Question 6

Find the probability.
-Two dice are rolled. Find the probability that the score on the dice is no more than 3.

Accepted Answer

A)  $\frac { 1 } { 12 }$ 
B)  $\frac { 1 } { 9 }$ 
C)  $\frac { 1 } { 18 }$ 
D)  $\frac { 5 } { 36 }$ 
A)  $\frac { 1 } { 12 }$ 
B)  $\frac { 1 } { 9 }$ 
C)  $\frac { 1 } { 18 }$ 
D)  $\frac { 5 } { 36 }$

Question 7

Determine the number of outcomes as requested.
-Two 6-sided dice are thrown. Determine the number of ways that a score of either 3 or 4 can be obtained.

Accepted Answer

A) 5 
B) 4 
C) 2 
D) 3 
A) 5 
B) 4 
C) 2 
D) 3

Question 8

Find the probability.
-If you are dealt two cards successively (with replacement of the first)from a standard 52-card deck, find the probability of getting a heart on the first card and a diamond on the second.

Accepted Answer

A)  $\frac { 13 } { 204 }$ 
B)  $\frac { 1 } { 204 }$ 
C)  $\frac { 1 } { 169 }$ 
D)  $\frac { 1 } { 16 }$ 
A)  $\frac { 13 } { 204 }$ 
B)  $\frac { 1 } { 204 }$ 
C)  $\frac { 1 } { 169 }$ 
D)  $\frac { 1 } { 16 }$

Question 9

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

Accepted Answer

A)  $\frac { 1 } { 14 }$ 
B)  $\frac { 1 } { 28 }$ 
C)  $\frac { 1 } { 16 }$ 
D)  $\frac { 1 } { 4 }$ 
A)  $\frac { 1 } { 14 }$ 
B)  $\frac { 1 } { 28 }$ 
C)  $\frac { 1 } { 16 }$ 
D)  $\frac { 1 } { 4 }$

Question 10

Find the requested probability.
-A box contains the following mixture of colored marbles: 2 black, 3 red, 5 yellow, and 2 green. If two marbles are drawn, the second being drawn after the first is replaced, then what is the Probability that both are black?

Accepted Answer

A)  $\frac { 1 } { 66 }$ 
B)  $\frac { 1 } { 36 }$ 
C)  $\frac { 1 } { 72 }$ 
D)  $\frac { 1 } { 132 }$ 
A)  $\frac { 1 } { 66 }$ 
B)  $\frac { 1 } { 36 }$ 
C)  $\frac { 1 } { 72 }$ 
D)  $\frac { 1 } { 132 }$

Question 11

Find the probability.
-Two dice are rolled. Find the probability that the score on the dice is either 5 or 10.

Accepted Answer

A)  $\frac { 7 } { 18 }$ 
B)  $\frac { 7 } { 36 }$ 
C)  $\frac { 1 } { 6 }$ 
D)  $\frac { 5 } { 12 }$ 
A)  $\frac { 7 } { 18 }$ 
B)  $\frac { 7 } { 36 }$ 
C)  $\frac { 1 } { 6 }$ 
D)  $\frac { 5 } { 12 }$

Question 12

Find the probability.
-Two dice are rolled. Find the probability that the score on the dice is 5.

Accepted Answer

A)  $\frac { 5 } { 12 }$ 
B)  $\frac { 1 } { 6 }$ 
C)  $\frac { 5 } { 36 }$ 
D)  $\frac { 1 } { 9 }$ 
A)  $\frac { 5 } { 12 }$ 
B)  $\frac { 1 } { 6 }$ 
C)  $\frac { 5 } { 36 }$ 
D)  $\frac { 1 } { 9 }$

Question 13

Find the probability.
-When a single card is drawn from an ordinary 52-card deck, find the probability of getting a black 9 or a black 7.

Accepted Answer

A)  $\frac { 1 } { 4 }$ 
B)  $\frac { 1 } { 52 }$ 
C)  $\frac { 1 } { 13 }$ 
D)  $\frac { 1 } { 26 }$ 
A)  $\frac { 1 } { 4 }$ 
B)  $\frac { 1 } { 52 }$ 
C)  $\frac { 1 } { 13 }$ 
D)  $\frac { 1 } { 26 }$

Question 14

Find the probability.
-Container A has balls numbered 1 through 8. Container B has balls numbered 1 through 4. What is the probability that a 4 is drawn from A followed by a 2 from B?

Accepted Answer

A)  $\frac { 1 } { 8 }$ 
B)  $\frac { 1 } { 32 }$ 
C)  $\frac { 3 } { 8 }$ 
D)  $\frac { 1 } { 16 }$ 
A)  $\frac { 1 } { 8 }$ 
B)  $\frac { 1 } { 32 }$ 
C)  $\frac { 3 } { 8 }$ 
D)  $\frac { 1 } { 16 }$

Question 15

Find the probability.
-When a single card is drawn from an ordinary 52-card deck, find the probability of getting a red card.

Accepted Answer

A)  $\frac { 1 } { 4 }$ 
B)  $\frac { 1 } { 52 }$ 
C)  2 
D)  $\frac { 1 } { 2 }$ 
A)  $\frac { 1 } { 4 }$ 
B)  $\frac { 1 } { 52 }$ 
C)  2 
D)  $\frac { 1 } { 2 }$

Question 16

Find the requested probability.
-A box contains the following mixture of colored marbles: 2 black, 1 red, 4 yellow, and 2 green. If two marbles are drawn, the second being drawn after the first is replaced, then what is the Probability that both are yellow?

Accepted Answer

A)  $\frac { 1 } { 72 }$ 
B)  $\frac { 1 } { 6 }$ 
C)  $\frac { 16 } { 81 }$ 
D)  $\frac { 4 } { 27 }$ 
A)  $\frac { 1 } { 72 }$ 
B)  $\frac { 1 } { 6 }$ 
C)  $\frac { 16 } { 81 }$ 
D)  $\frac { 4 } { 27 }$

Question 17

Solve the problem.
-The following list of digits was taken from a table of random numbers. We will let each set of 5 represent a family of five children. If a digit is 0 - 4 it will be a girl and the digit 5 - 9 will be a boy.
Use this simulation to estimate the probability that a family of five children will have less than 2 boys. $\begin{array}{lllll}
18728 & 94741 & 32063 & 04963 & 54859 \
15592 & 71357 & 28152 & 11732 & 17173 \
89555 & 75520 & 08882 & 95295 & 72895 \
38894 & 58070 & 77371 & 10194 & 94917 \
64336 & 95103 & 90740 & 03577 & 62599
\end{array}$

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

Accepted Answer

A)  $\frac { 8 } { 50 }$ 
B)  None of these 
C)  $\frac { 12 } { 50 }$ 
D)  $\frac { 3 } { 10 }$ 
A)  $\frac { 8 } { 50 }$ 
B)  None of these 
C)  $\frac { 12 } { 50 }$ 
D)  $\frac { 3 } { 10 }$

Question 18

Solve the problem.
-A lottery game has balls numbered 1 through 19. What is the probability of selecting an even numbered ball or a 4?

Accepted Answer

A) 4 : 15 
B) 9 : 19 
C) 19 : -15 
D) 9 : 10 
A) 4 : 15 
B) 9 : 19 
C) 19 : -15 
D) 9 : 10

Question 19

Solve the problem.
-What is the probability of spinning an A on this spinner?

Accepted Answer

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

Question 20

Solve the problem.
-In the past, Michael has had the following success when shooting after having been fouled.  30% ,  30% , and  40%  of the time he will get 0,1 , or 2 points. Which of the following simulations could be used for estimating the probabilities of shooting 0,1 or 2 points?

Accepted Answer

A)  None of these 
B)   0 - 3=1  point,  4 - 6=2  points, and  7 - 9=0  points 
C)  It is not possible to create a simulation 
D)   0 - 2=1  point,  3 - 6=2  points, with the digits  0 - 9 . and  7 - 9=0  points 
A)  None of these 
B)   0 - 3=1  point,  4 - 6=2  points, and  7 - 9=0  points 
C)  It is not possible to create a simulation 
D)   0 - 2=1  point,  3 - 6=2  points, with the digits  0 - 9 . and  7 - 9=0  points

Solve the problem. -Assume that the probability is $\frac { 1 } { 2 }$ that a child born is a boy. What is the probability that both of a family's two children are girls?

Solve the problem. -What is the probability of a dart landing in the shaded region? (Assume that the x's represent equal measures and that the dart is equally likely to land in any region on The board.)

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

Solve the problem. -The following string of B's and G's was obtained from tossing a quarter 40 times. Heads were listed as B and tails as G . Use this simulation to estimate the probability of two girls being born in succession. $\{ \text { BBGGGGGBGGBBGGGBGGBBBGBBGBBBBGGBBGGBGGBG } \}$

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 red.

Find the probability. -Two dice are rolled. Find the probability that the score on the dice is no more than 3.

Determine the number of outcomes as requested. -Two 6-sided dice are thrown. Determine the number of ways that a score of either 3 or 4 can be obtained.

Find the probability. -If you are dealt two cards successively (with replacement of the first)from a standard 52-card deck, find the probability of getting a heart on the first card and a diamond on the second.

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

Find the requested probability. -A box contains the following mixture of colored marbles: 2 black, 3 red, 5 yellow, and 2 green. If two marbles are drawn, the second being drawn after the first is replaced, then what is the Probability that both are black?

Find the probability. -Two dice are rolled. Find the probability that the score on the dice is either 5 or 10.

Find the probability. -Two dice are rolled. Find the probability that the score on the dice is 5.

Find the probability. -When a single card is drawn from an ordinary 52-card deck, find the probability of getting a black 9 or a black 7.

Find the probability. -Container A has balls numbered 1 through 8. Container B has balls numbered 1 through 4. What is the probability that a 4 is drawn from A followed by a 2 from B?

Find the probability. -When a single card is drawn from an ordinary 52-card deck, find the probability of getting a red card.

Find the requested probability. -A box contains the following mixture of colored marbles: 2 black, 1 red, 4 yellow, and 2 green. If two marbles are drawn, the second being drawn after the first is replaced, then what is the Probability that both are yellow?

Solve the problem. -A lottery game has balls numbered 1 through 19. What is the probability of selecting an even numbered ball or a 4?

Solve the problem. -What is the probability of spinning an A on this spinner?

Solve the problem. -In the past, Michael has had the following success when shooting after having been fouled. 30% , 30% , and 40% of the time he will get 0,1 , or 2 points. Which of the following simulations could be used for estimating the probabilities of shooting 0,1 or 2 points?

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

Solve the problem. -Assume that the probability is 12\frac { 1 } { 2 }21​ that a child born is a boy. What is the probability that both of a family's two children are girls?