Question 1

Solve the problem.
-Assume that a person spins the pointer and is awarded the amount indicated by the pointer. Determine the personʹs expectation.

Accepted Answer

A)  $5.25 
B)  $10.50 
C)  $7.25 
D)  $7.50 
A)  $5.25 
B)  $10.50 
C)  $7.25 
D)  $7.50

Question 2

Solve the problem.
-A couple plans to have four children. Using a tree diagram , obtain the sample space. Then, find The probability that the family has three boys first and then one girl.

Accepted Answer

A)  $\frac { 1 } { 6 }$ 
B)  $\frac { 1 } { 8 }$ 
C)  $\frac { 3 } { 16 }$ 
D)  $\frac { 1 } { 16 }$ 
A)  $\frac { 1 } { 6 }$ 
B)  $\frac { 1 } { 8 }$ 
C)  $\frac { 3 } { 16 }$ 
D)  $\frac { 1 } { 16 }$

Question 3

Use the counting principle to obtain the answer.
-A sports shop sold tennis rackets in 4 different weights, 3 types of string, and 3 grip sizes. How Many different rackets could they sell?

Accepted Answer

A)  10 
B)  48 
C)  36 
D)  21 
A)  10 
B)  48 
C)  36 
D)  21

Question 4

Find the probability.
-What is the probability that 8 rolls of a fair die will show three threes? Round to the nearest Ten-thousandth.

Accepted Answer

A)  0.1042 
B)  0.0208 
C)  0.2084 
D)  0.0521 
A)  0.1042 
B)  0.0208 
C)  0.2084 
D)  0.0521

Question 5

Find the probability. Round to the nearest ten-thousandth when necessary.
-A family has five children. The probability of having a girl is 1/2. What is the probability of having Exactly 2 girls and 3 boys?

Accepted Answer

A)  0.0625 
B)  0.0312 
C)  0.6252 
D)  0.3125 
A)  0.0625 
B)  0.0312 
C)  0.6252 
D)  0.3125

Question 6

Use the table to find the probability.
-The following table indicates the preference for different types of soft drinks by three age groups. $\begin{array}{r|rrr} 
& \text { cola } & \text { root beer } & \text { lemon-lime } \
\hline \text { under 21 years of age } & 40 & 25 & 20 \
\text { between 21 and 40 } & 35 & 20 & 30 \
\text { over 40 years of age } & 20 & 30 & 35
\end{array}$

If a person is selected at random, find the probability that the person is over 40 years of age.

Accepted Answer

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

Question 7

Find the probability. Round to the nearest ten-thousandth when necessary.
-A bag contains 6 cherry, 3 orange, and 2 lemon candies. You reach in and take 3 pieces of candy at Random. Find the probability that you have 2 orange candies and 1 lemon candy.

Accepted Answer

A)  0.0364 
B)  0.0303 
C)  0.1091 
D)  0.3636 
A)  0.0364 
B)  0.0303 
C)  0.1091 
D)  0.3636

Question 8

Solve the problem.
-Bob and Fred play the following game. Bob rolls a single die. If an even number results, Bob must Pay Fred the number of dollars indicated by the number rolled. On the other hand, if an odd Number is rolled, Fred must pay Bob the number of dollars indicated by the number rolled. Find Fredʹs expectation.

Accepted Answer

A)  $0.00 
B)  -$0.10 
C)  $0.50 
D)  $0.25 
A)  $0.00 
B)  -$0.10 
C)  $0.50 
D)  $0.25

Question 9

Solve the problem.
-How many different 4-letter radio-station call letters can be made if the first letter must be K or W, Repeats are allowed, but the call letters cannot end in an O?

Accepted Answer

A)  35,152 
B)  16,900 
C)  33,800 
D)  456,976 
A)  35,152 
B)  16,900 
C)  33,800 
D)  456,976

Question 10

Find the probability.
-A number cube labeled with numbers 1, 2, 3, 4, 5, and 6 is tossed. What are the odds in favor of the Cube showing a 4?

Accepted Answer

A)  1:5 
B)  1:6 
C)  2:3 
D)  1:4 
A)  1:5 
B)  1:6 
C)  2:3 
D)  1:4

Question 11

Assume that each of the n trials is independent and that p is the probability of success on a given trial. Use the binomial probability formula to find P(x). Round to four decimal places.
-$$\mathrm { n } = 16 , \mathrm { x } = 3 , \mathrm { p } = \frac { 1 } { 5 }$$

Accepted Answer

A)  0.2709 
B)  0.3202 
C)  0.2463 
D)  0.2955 
A)  0.2709 
B)  0.3202 
C)  0.2463 
D)  0.2955

Question 12

Use the table to find the probability.
-The following table contains data from a study of two airlines which fly to Small Town, USA. $\begin{array}{l|cc} 
& \begin{array}{r}
\text { Number of flights } \
\text { arrived on time }
\end{array} & \begin{array}{r}
\text { Number of flights } \
\text { arrived late }
\end{array} \
\hline \text { Podunk Airlines } & 33 & 6 \
\text { Upstate Airlines } & 43 & 5
\end{array}$
If a flight is selected at random, find the probability that the flight will arrive on time given that they fly with Upstate airlines.

Accepted Answer

A)  $\frac { 11 } { 76 }$ 
B)  $\frac { 43 } { 48 }$ 
C)  $\frac { 43 } { 87 }$ 
D)  None of the above is correct. 
A)  $\frac { 11 } { 76 }$ 
B)  $\frac { 43 } { 48 }$ 
C)  $\frac { 43 } { 87 }$ 
D)  None of the above is correct.

Question 13

Solve the problem.
-A student is taking a standardized test consisting of multiple choice questions for which there are Five options for each question. Five points are awarded for each correct answer, but the student Loses 2 points for an incorrect answer. Questions left blank neither receive nor lose points. What is The minimum number of options that the student should be able to rule out before making a guess On any particular question?

Accepted Answer

A)  Three 
B)  Two 
C)  One 
D)  None 
A)  Three 
B)  Two 
C)  One 
D)  None

Question 14

Solve the problem.
-A card is drawn at random from a well-shuffled deck of 52 cards. What is the probability of Drawing a face card or a spade?

Accepted Answer

A)  $\frac { 6 } { 13 }$ 
B)  $\frac { 1 } { 2 }$ 
C)  $\frac { 11 } { 26 }$ 
D)  $\frac { 25 } { 52 }$ 
A)  $\frac { 6 } { 13 }$ 
B)  $\frac { 1 } { 2 }$ 
C)  $\frac { 11 } { 26 }$ 
D)  $\frac { 25 } { 52 }$

Question 15

Solve the problem.
-If two cards are drawn without replacement from a deck, find the probability that the second card Is red, given that the first card was a heart.

Accepted Answer

A)  $\frac { 12 } { 51 }$ 
B)  $\frac { 25 } { 51 }$ 
C)  $\frac { 26 } { 51 }$ 
D)  $\frac { 22 } { 23 }$ 
A)  $\frac { 12 } { 51 }$ 
B)  $\frac { 25 } { 51 }$ 
C)  $\frac { 26 } { 51 }$ 
D)  $\frac { 22 } { 23 }$

Question 16

Solve the problem.
-If you toss four fair coins, in how many ways can you obtain at least one head?

Accepted Answer

A)  16 
B)  15 
C)  5 
D)  4 
A)  16 
B)  15 
C)  5 
D)  4

Question 17

Solve the problem.
-This spinner is spun 36 times. The spinner landed on A 1 time, on B 4 times, and on C 31 times. Compute the empirical probability that the spinner will land on B.

Accepted Answer

A)  $\frac { 1 } { 9 }$ 
B)  $\frac { 35 } { 36 }$ 
C)  $\frac { 1 } { 3 }$ 
D)  $\frac { 1 } { 4 }$ 
A)  $\frac { 1 } { 9 }$ 
B)  $\frac { 35 } { 36 }$ 
C)  $\frac { 1 } { 3 }$ 
D)  $\frac { 1 } { 4 }$

Question 18

Solve the problem.
-How many different three-number ʺcombinationsʺ are possible on a combination lock having 22 Numbers on its dial? Assume that no numbers repeat. (Combination locks are really permutation Locks.)

Accepted Answer

A)  9240 
B)  1,053,400 
C)  351,120 
D)  175,560 
A)  9240 
B)  1,053,400 
C)  351,120 
D)  175,560

Question 19

Solve the problem.
-A bag contains 6 apples and 4 oranges. If you select 5 pieces of fruit without looking, how many Ways can you get 5 apples?

Accepted Answer

A)  12 
B)  6 
C)  24 
D)  10 
A)  12 
B)  6 
C)  24 
D)  10

Question 20

Find the probability of the following five-card poker hands from a 52-card deck. In poker, aces are either high or low.
-Flush (5 in same suit, but not a straight flush)

Accepted Answer

A)  $\frac { 33 } { 66640 }$ 
B)  $\frac { 1247 } { 2598960 }$ 
C)  $\frac { 1277 } { 649740 }$ 
D)  $\frac { 33 } { 16660 }$ 
A)  $\frac { 33 } { 66640 }$ 
B)  $\frac { 1247 } { 2598960 }$ 
C)  $\frac { 1277 } { 649740 }$ 
D)  $\frac { 33 } { 16660 }$

Solve the problem. -Assume that a person spins the pointer and is awarded the amount indicated by the pointer. Determine the personʹs expectation.

Solve the problem. -A couple plans to have four children. Using a tree diagram , obtain the sample space. Then, find The probability that the family has three boys first and then one girl.

Use the counting principle to obtain the answer. -A sports shop sold tennis rackets in 4 different weights, 3 types of string, and 3 grip sizes. How Many different rackets could they sell?

Find the probability. -What is the probability that 8 rolls of a fair die will show three threes? Round to the nearest Ten-thousandth.

Find the probability. Round to the nearest ten-thousandth when necessary. -A family has five children. The probability of having a girl is 1/2. What is the probability of having Exactly 2 girls and 3 boys?

Find the probability. Round to the nearest ten-thousandth when necessary. -A bag contains 6 cherry, 3 orange, and 2 lemon candies. You reach in and take 3 pieces of candy at Random. Find the probability that you have 2 orange candies and 1 lemon candy.

Solve the problem. -How many different 4-letter radio-station call letters can be made if the first letter must be K or W, Repeats are allowed, but the call letters cannot end in an O?

Find the probability. -A number cube labeled with numbers 1, 2, 3, 4, 5, and 6 is tossed. What are the odds in favor of the Cube showing a 4?

Assume that each of the n trials is independent and that p is the probability of success on a given trial. Use the binomial probability formula to find P(x). Round to four decimal places. - $\mathrm { n } = 16 , \mathrm { x } = 3 , \mathrm { p } = \frac { 1 } { 5 }$

Solve the problem. -A card is drawn at random from a well-shuffled deck of 52 cards. What is the probability of Drawing a face card or a spade?

Solve the problem. -If two cards are drawn without replacement from a deck, find the probability that the second card Is red, given that the first card was a heart.

Solve the problem. -If you toss four fair coins, in how many ways can you obtain at least one head?

Solve the problem. -This spinner is spun 36 times. The spinner landed on A 1 time, on B 4 times, and on C 31 times. Compute the empirical probability that the spinner will land on B.

Solve the problem. -How many different three-number ʺcombinationsʺ are possible on a combination lock having 22 Numbers on its dial? Assume that no numbers repeat. (Combination locks are really permutation Locks.)

Solve the problem. -A bag contains 6 apples and 4 oranges. If you select 5 pieces of fruit without looking, how many Ways can you get 5 apples?

Find the probability of the following five-card poker hands from a 52-card deck. In poker, aces are either high or low. -Flush (5 in same suit, but not a straight flush)

Critical Thinking Skills

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Number Theory and the Real Number System

Algebra, Graphs, and Functions

The Metric System

Geometry

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Exam 11: Probability