Question 1

Decide whether or not the events are mutually exclusive.
-Being a teenager and being a United States Senator

Accepted Answer

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

Question 2

Find the indicated probability.
-The following table contains data from a study of two airlines which fly to Small Town, USA.  
If one of the 87 flights is randomly selected, find the probability that the flight selected is an Upstate Airlines flight given that it was late.

Accepted Answer

A)  $\frac { 5 } { 11 }$ 
B)  $\frac { 5 } { 87 }$ 
C)  $\frac { 5 } { 48 }$ 
D)  None of the above is correct. 
A)  $\frac { 5 } { 11 }$ 
B)  $\frac { 5 } { 87 }$ 
C)  $\frac { 5 } { 48 }$ 
D)  None of the above is correct. A

Question 3

Give the probability that the spinner shown would land on the indicated color.
-black

Accepted Answer

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

Question 4

Find the probability.
-A family has five children. The probability of having a girl is 1/2. What is the probability of having 3 girls followed by 2 boys?

Accepted Answer

A)  $\frac { 1 } { 16 }$ 
B)  $\frac { 1 } { 32 }$ 
C)  $\frac { 1 } { 120 }$ 
D)  $\frac { 5 } { 16 }$ 
A)  $\frac { 1 } { 16 }$ 
B)  $\frac { 1 } { 32 }$ 
C)  $\frac { 1 } { 120 }$ 
D)  $\frac { 5 } { 16 }$

Question 5

Find the indicated probability.
-The distribution of B.A. degrees conferred by a local college is listed below, by major. $$\begin{array} { l r } 
\underline { \text { Major } } & \text { Frequency } \
\text { English } & 2073 \
\text { Mathematics } & 2164 \
\text { Chemistry } & 318 \
\text { Physics } & 856 \
\text { Liberal Arts } & 1358 \
\text { Business } & 1676 \
\text { Engineering } & 868 \
& 9313
\end{array}$$ What is the probability that a randomly selected degree is in English or Mathematics?

Accepted Answer

A) 0.424 
B) 0.010 
C) 0.455 
D) 0.517 
A) 0.424 
B) 0.010 
C) 0.455 
D) 0.517

Question 6

Find the probability.
-When two balanced dice are rolled, there are 36 possible outcomes. What is the probability that the sum of the numbers on the dice is 6 or 9?

Accepted Answer

A)  $\frac { 1 } { 54 }$ 
B)  $\frac { 1 } { 4 }$ 
C)  $\frac { 5 } { 12 }$ 
D)  $\frac { 3 } { 2 }$ 
A)  $\frac { 1 } { 54 }$ 
B)  $\frac { 1 } { 4 }$ 
C)  $\frac { 5 } { 12 }$ 
D)  $\frac { 3 } { 2 }$

Question 7

The results of a school election for student president are shown in the following table. $$\begin{array} { l | l l l l l } 
\text { Candidate } & \text { A } & \text { B } & \text { C } & \text { D } & \text { E } \
\hline \text { Votes for } & 12 & 24 & 21 & 29 & 14
\end{array}$$ What is the probability that a randomly polled voter voted for Candidate C?

Accepted Answer

A) 0.50 
B) 0.21 
C) 0.12 
D) 0.29 
A) 0.50 
B) 0.21 
C) 0.12 
D) 0.29

Question 8

Use the general multiplication rule to find the indicated probability.
-You are dealt two cards successively (without replacement)from a shuffled deck of 52 playing cards. Find the probability that both cards are black.

Accepted Answer

A)  $\frac { 13 } { 51 }$ 
B)  $\frac { 25 } { 102 }$ 
C)  $\frac { 1 } { 2652 }$ 
D)  $\frac { 25 } { 51 }$ 
A)  $\frac { 13 } { 51 }$ 
B)  $\frac { 25 } { 102 }$ 
C)  $\frac { 1 } { 2652 }$ 
D)  $\frac { 25 } { 51 }$

Question 9

Solve the problem.
-Four boys and three girls are seated in a row, at random, to watch a play. What is the probability that a girl is seated at each end of the row?

Accepted Answer

A)  $\frac { 1 } { 14 }$ 
B)  $\frac { 2 } { 7 }$ 
C)  $\frac { 3 } { 7 }$ 
D)  $\frac { 1 } { 7 }$ 
A)  $\frac { 1 } { 14 }$ 
B)  $\frac { 2 } { 7 }$ 
C)  $\frac { 3 } { 7 }$ 
D)  $\frac { 1 } { 7 }$

Question 10

A sample of 4 different calculators is randomly selected from a group containing 35 that are defective and 27 that have no defects. What is the probability that all four of the calculators selected
Are defective?

Accepted Answer

A) 0.3541 
B) 2.9835 
C) 0.0939 
D) 0.1016 
A) 0.3541 
B) 2.9835 
C) 0.0939 
D) 0.1016

Question 11

Find the conditional probability.
-Suppose one card is selected at random from an ordinary deck of 52 playing cards. Let A = event a queen is selected
B = event a diamond is selected. Determine $\mathrm { P } ( \mathrm { B } \mid \mathrm { A } )$.

Accepted Answer

A)  $\frac { 1 } { 13 }$ 
B)  $\frac { 1 } { 4 }$ 
C)  $\frac { 1 } { 2 }$ 
D)  $\frac { 1 } { 52 }$ 
A)  $\frac { 1 } { 13 }$ 
B)  $\frac { 1 } { 4 }$ 
C)  $\frac { 1 } { 2 }$ 
D)  $\frac { 1 } { 52 }$

Question 12

Find the indicated probability.
-The age distribution of students at a community college is given below. $$\begin{array} { l r } 
\text { Age (years) } & \text { Number of students (f) } \
\hline \text { Under 21 } & 400 \
21 - 25 & 403 \
26 - 30 & 219 \
31 - 35 & 56 \
\text { Over 35 } & 29 \
\hline & 1107
\end{array}$$ A student from the community college is selected at random. Find the probability that the student is between 26 and 35 inclusive. Round approximations to three decimal places.

Accepted Answer

A) 0.198 
B) 0.248 
C) 0.051 
D) 275 
A) 0.198 
B) 0.248 
C) 0.051 
D) 275

Question 13

Find the probability of the following card hands from a 52-card deck. In poker, aces are either high or low. A bridge hand is made up of 13 cards.
-In poker, a flush (5 in same suit)in any suit

Accepted Answer

A) 0.00198 
B) 0.000347 
C) 0.00122 
D) 0.000495 
A) 0.00198 
B) 0.000347 
C) 0.00122 
D) 0.000495

Question 14

Find the probability.
-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?

Accepted Answer

A)  $\frac { 10 } { 9 }$ 
B)  $\frac { 1 } { 3 }$ 
C)  $\frac { 2 } { 3 }$ 
D)  17 
A)  $\frac { 10 } { 9 }$ 
B)  $\frac { 1 } { 3 }$ 
C)  $\frac { 2 } { 3 }$ 
D)  17

Question 15

Solve the problem.
-What are t   he odds against drawing a number greater than 2 from these cards?

Accepted Answer

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

Question 16

Determine whether the events are independent.
-A card is selected at random from a standard deck of 52 cards. It is then replaced and a second card is selected at random. Are the events "club on the first draw" and "ace on the second draw"
Independent?

Accepted Answer

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

Question 17

Determine whether the events are independent.
-A bag contains 9 red and 8 green marbles. A marble is drawn, replaced in the bag, then a second marble is drawn. Are the events "first marble is red" and "second marble is green" independent
Events?

Accepted Answer

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

Question 18

The table shows the number of college students who prefer a given pizza topping. $$\begin{array} { r | r r r r } 
\text { toppings } & \text { freshman } & \text { sophomore } & \text { junior } & \text { senior } \
\hline \text { cheese } & 16 & 16 & 21 & 28 \
\text { meat } & 24 & 28 & 16 & 16 \
\text { veggie } & 16 & 16 & 24 & 28
\end{array}$$ Find the empirical probability that a randomly selected student prefers cheese toppings.

Accepted Answer

A) 0.325 
B) 0.337 
C) 0.346 
D) 0.112 
A) 0.325 
B) 0.337 
C) 0.346 
D) 0.112

Question 19

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 face card on the first card and an ace on the second.

Accepted Answer

A)  $\frac { 4 } { 221 }$ 
B)  $\frac { 3 } { 169 }$ 
C)  $\frac { 4 } { 13 }$ 
D)  $\frac { 9 } { 169 }$ 
A)  $\frac { 4 } { 221 }$ 
B)  $\frac { 3 } { 169 }$ 
C)  $\frac { 4 } { 13 }$ 
D)  $\frac { 9 } { 169 }$

Question 20

Find the indicated probability.
-A card is drawn at random from a standard 52-card deck. Find the probability that the card is not a queen.

Accepted Answer

A)  $\frac { 3 } { 4 }$ 
B)  $\frac { 12 } { 13 }$ 
C)  $\frac { 1 } { 4 }$ 
D)  $\frac { 1 } { 13 }$ 
A)  $\frac { 3 } { 4 }$ 
B)  $\frac { 12 } { 13 }$ 
C)  $\frac { 1 } { 4 }$ 
D)  $\frac { 1 } { 13 }$

Decide whether or not the events are mutually exclusive. -Being a teenager and being a United States Senator

Find the indicated probability. -The following table contains data from a study of two airlines which fly to Small Town, USA. If one of the 87 flights is randomly selected, find the probability that the flight selected is an Upstate Airlines flight given that it was late.

Give the probability that the spinner shown would land on the indicated color. -black

Find the probability. -A family has five children. The probability of having a girl is 1/2. What is the probability of having 3 girls followed by 2 boys?

Find the probability. -When two balanced dice are rolled, there are 36 possible outcomes. What is the probability that the sum of the numbers on the dice is 6 or 9?

The results of a school election for student president are shown in the following table. Candidate A B C D E Votes for 12 24 21 29 14 What is the probability that a randomly polled voter voted for Candidate C?

Use the general multiplication rule to find the indicated probability. -You are dealt two cards successively (without replacement)from a shuffled deck of 52 playing cards. Find the probability that both cards are black.

Solve the problem. -Four boys and three girls are seated in a row, at random, to watch a play. What is the probability that a girl is seated at each end of the row?

A sample of 4 different calculators is randomly selected from a group containing 35 that are defective and 27 that have no defects. What is the probability that all four of the calculators selected Are defective?

Find the conditional probability. -Suppose one card is selected at random from an ordinary deck of 52 playing cards. Let A = event a queen is selected B = event a diamond is selected. Determine $\mathrm { P } ( \mathrm { B } \mid \mathrm { A } )$ .

Find the probability of the following card hands from a 52-card deck. In poker, aces are either high or low. A bridge hand is made up of 13 cards. -In poker, a flush (5 in same suit)in any suit

Find the probability. -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?

Solve the problem. -What are t he odds against drawing a number greater than 2 from these cards?

Determine whether the events are independent. -A card is selected at random from a standard deck of 52 cards. It is then replaced and a second card is selected at random. Are the events "club on the first draw" and "ace on the second draw" Independent?

Determine whether the events are independent. -A bag contains 9 red and 8 green marbles. A marble is drawn, replaced in the bag, then a second marble is drawn. Are the events "first marble is red" and "second marble is green" independent Events?

The table shows the number of college students who prefer a given pizza topping. toppings freshman sophomore junior senior cheese 16 16 21 28 meat 24 28 16 16 veggie 16 16 24 28 Find the empirical probability that a randomly selected student prefers cheese toppings.

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 face card on the first card and an ace on the second.

Find the indicated probability. -A card is drawn at random from a standard 52-card deck. Find the probability that the card is not a queen.

The Art of Problem Solving

The Basic Concepts of Set Theory

Introduction to Logic

Numeration Systems

Number Theory

The Real Numbers and Their Representations

The Basic Concepts of Algebra

Graphs, Functions, and Systems of Equations and Inequalities

Geometry

Counting Methods

Statistics

Personal Financial Management

Trigonometry Formerly

Graph Theory

Voting and Apportionment

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Exam 11: Probability