Question 1

In a London State daily lottery, a sequence of 3 (not necessarily different) digits in the range 0-7 are selected at random. Find the probability that 2 of 3 digits are the same.

Accepted Answer

A)  $\frac { 1 } { 2 }$ 
B)  $\frac { 3 } { 8 }$ 
C)  $\frac { 35 } { 384 }$ 
D)  $\frac { 7 } { 256 }$ 
E)  $\frac { 21 } { 64 }$ 
A)  $\frac { 1 } { 2 }$ 
B)  $\frac { 3 } { 8 }$ 
C)  $\frac { 35 } { 384 }$ 
D)  $\frac { 7 } { 256 }$ 
E)  $\frac { 21 } { 64 }$

Question 2

My couch potato friend enjoys sitting in front of the TV and grabbing handfuls of three chocolates at random from his snack jar. Unbeknownst to him, I have replaced 1 of the ten chocolates in his jar with a cashew. (He hates cashews with a passion!) How many possible outcomes are there the first time he grabs three chocolates  How many of these include the cashew

Accepted Answer

A) 120  outcomes, and 12 include the cashew 
B)  242 outcomes, and 36 include the cashew 
C)  120  outcomes, and 36 include the cashew 
D)   720 outcomes, and 72 include the cashew 
E)  84  outcomes, and 12 include the cashew 
A) 120  outcomes, and 12 include the cashew 
B)  242 outcomes, and 36 include the cashew 
C)  120  outcomes, and 36 include the cashew 
D)   720 outcomes, and 72 include the cashew 
E)  84  outcomes, and 12 include the cashew

Question 3

The following table shows the results of a survey of authors by a (fictitious) publishing company: $$\begin{array} { | l | l | l | l | } 
\hline & \text { New Authors } & \begin{array} { l } 
\text { Established } \
\text { Authors }
\end{array} & \text { Total } \
\hline \text { Successful } & 5 & 25 & 30 \
\hline \text { Unsuccessful } & 15 & 55 & 70 \
\hline \text { Total } & 20 & 80 & 100 \
\hline
\end{array}$$   Consider the following events:
S: An author is successful; U: An author is unsuccessful; N: An author is new; and E: An author is established.
Which of the following pairs of events are mutually exclusive:

Accepted Answer

A) N and S 
B)  both S and E, and N and E 
C)  S and E 
D)  both S and E, and N and S 
E)  N and E 
A) N and S 
B)  both S and E, and N and E 
C)  S and E 
D)  both S and E, and N and S 
E)  N and E

Question 4

A pair of dice is cast, and the number that appears uppermost on each die is observed.
​
Find the probability of the event that the sum of the numbers is 9.

Accepted Answer

The answer of A pair of dice is cast, and...

Question 5

A local TV station employs Desmorelda, "Mistress of the Zodiac", as its weather forecaster. Now, when it rains, Sagittarius is in the shadow of Jupiter one-fourth of the time, and it rains on 5 out of every 50 days. Sagittarius falls in Jupiter's shadow on only one in every six rainless days. The powers that be at the station notice a disturbing pattern to Desmorelda's weather predictions. It seems that she always predicts that it will rain when Sagittarius is in the shadow of Jupiter. What percentage of the time is she correct  Round your answer to the nearest 1%.

Accepted Answer

A) 18% 
B)  14% 
C)  13% 
D)  15% 
E)  10% 
A) 18% 
B)  14% 
C)  13% 
D)  15% 
E)  10%

Question 6

Compute the following quantities.   $$P ( A \cap C )$$ , $$P ( A \cap D )$$ , $$P ( B \cap C )$$ , and $$P ( B \cap D )$$

Accepted Answer

A)  $P ( A \cap C ) = 0.16$ , $P ( A \cap D ) = 0.24$ , $P ( B \cap C ) = 0.18$ , and $P ( B \cap D ) = 0.42$ 
B)  $P ( A \cap C ) = 0.15$ , $P ( A \cap D ) = 0.22$ , $P ( B \cap C ) = 0.19$ , and $P ( B \cap D ) = 0.45$ 
C)  $P ( A \cap C ) = 0.14$ , $P ( A \cap D ) = 0.24$ , $P ( B \cap C ) = 0.15$ , and $P ( B \cap D ) = 0.42$ 
D)  $P ( A \cap C ) = 0.14$ , $P ( A \cap D ) = 0.22$ , $P ( B \cap C ) = 0.15$ , and $P ( B \cap D ) = 0.45$ 
E)  $P ( A \cap C ) = 0.15$ , $P ( A \cap D ) = 0.23$ , $P ( B \cap C ) = 0.19$ , and $P ( B \cap D ) = 0.41$ 
A)  $P ( A \cap C ) = 0.16$ , $P ( A \cap D ) = 0.24$ , $P ( B \cap C ) = 0.18$ , and $P ( B \cap D ) = 0.42$ 
B)  $P ( A \cap C ) = 0.15$ , $P ( A \cap D ) = 0.22$ , $P ( B \cap C ) = 0.19$ , and $P ( B \cap D ) = 0.45$ 
C)  $P ( A \cap C ) = 0.14$ , $P ( A \cap D ) = 0.24$ , $P ( B \cap C ) = 0.15$ , and $P ( B \cap D ) = 0.42$ 
D)  $P ( A \cap C ) = 0.14$ , $P ( A \cap D ) = 0.22$ , $P ( B \cap C ) = 0.15$ , and $P ( B \cap D ) = 0.45$ 
E)  $P ( A \cap C ) = 0.15$ , $P ( A \cap D ) = 0.23$ , $P ( B \cap C ) = 0.19$ , and $P ( B \cap D ) = 0.41$

Question 7

The Sad State Lottery requires you to select a sequence of three different numbers from zero through 48. (Order is important.) You are a winner if your sequence agrees with that drawing, and you are a booby prize winner if your selection of numbers is correct, but in the wrong order. What is the probability of being a winner  What is the probability that you are either a winner or a booby prize winner

Accepted Answer

A) The probability of being a winner is $\frac { 1 } { 110,544 }$ . The probability of being either a winner or a booby prize winner is $\frac { 1 } { 18,424 }$ . 
B)  The probability of being a winner is $\frac { 1 } { 110,544 }$ .
The probability of being either a winner or a booby prize winner is $\frac { 3 } { 9,212 }$ . 
C)  The probability of being a winner is $\frac { 5 } { 110,544 }$ .
The probability of being either a winner or a booby prize winner is $\frac { 3 } { 9,212 }$ . 
D)  The probability of being a winner is $\frac { 5 } { 48 }$ .
The probability of being either a winner or a booby prize winner is $\frac { 3 } { 9,212 }$ . 
E)  The probability of being a winner is $\frac { 1 } { 18,424 }$ .
The probability of being either a winner or a booby prize winner is $\frac { 1 } { 18,424 }$ . 
A) The probability of being a winner is $\frac { 1 } { 110,544 }$ . The probability of being either a winner or a booby prize winner is $\frac { 1 } { 18,424 }$ . 
B)  The probability of being a winner is $\frac { 1 } { 110,544 }$ .
The probability of being either a winner or a booby prize winner is $\frac { 3 } { 9,212 }$ . 
C)  The probability of being a winner is $\frac { 5 } { 110,544 }$ .
The probability of being either a winner or a booby prize winner is $\frac { 3 } { 9,212 }$ . 
D)  The probability of being a winner is $\frac { 5 } { 48 }$ .
The probability of being either a winner or a booby prize winner is $\frac { 3 } { 9,212 }$ . 
E)  The probability of being a winner is $\frac { 1 } { 18,424 }$ .
The probability of being either a winner or a booby prize winner is $\frac { 1 } { 18,424 }$ .

Question 8

According to the New York Times/CBS poll of March, 2005, 47% agreed that Social Security taxes should be raised if necessary to keep the system afloat, and 42% agreed that it would be a good idea to invest part of their Social Security taxes on their own. What is the largest percentage of people who could have agreed with at least one of these statements  What is the smallest percentage of people who could have agreed with at least one of these statements  ?

Accepted Answer

A) The largest percentage is 88%, the smallest percentage is 48% 
B)  The largest percentage is 87%, the smallest percentage is 45% 
C)  The largest percentage is 89%, the smallest percentage is 47% 
D)  The largest percentage is 100%, the smallest percentage is 88% 
E)  The largest percentage is 100%, the smallest percentage is 87% 
A) The largest percentage is 88%, the smallest percentage is 48% 
B)  The largest percentage is 87%, the smallest percentage is 45% 
C)  The largest percentage is 89%, the smallest percentage is 47% 
D)  The largest percentage is 100%, the smallest percentage is 88% 
E)  The largest percentage is 100%, the smallest percentage is 87%

Question 9

The table shows the results of a survey of 100 authors by a publishing company. Compute the conditional probability: An author is established, given that she is successful. $$\begin{array} { | l | l | l | l | } 
\hline & \text { New Authors } & \begin{array} { l } 
\text { Established } \
\text { Authors }
\end{array} & \text { Total } \
\hline \text { Successful } & 5 & 26 & 31 \
\hline \text { Unsuccessful } & 14 & 55 & 69 \
\hline \text { Total } & 19 & 81 & 100 \
\hline
\end{array}$$

Accepted Answer

The answer of The table shows the results of a...

Question 10

The following table shows the results of a survey of 340 authors by a (fictitious) publishing company: $$\begin{array} { | l | l | l | l | } 
\hline & \begin{array} { l } 
\text { New } \
\text { Authors }
\end{array} & \begin{array} { l } 
\text { Established } \
\text { Authors }
\end{array} &{ \text { Total } } \
\hline \text { Successful } & 40 & 20 & 60 \
\hline \text { Unsuccessful } & 110 & 170 & 280 \
\hline \text { Total } & 150 & 190 & 340 \
\hline
\end{array}$$   An author is chosen at random.
Compute the estimated probability of the event that the author is unsuccessful and new.

Accepted Answer

A)   $\frac { 11 } { 34 }$ 
B)    $\frac { 1 } { 2 }$ 
C)    $\frac { 23 } { 34 }$ 
D)    $\frac { 11 } { 15 }$ 
E)    $\frac { 4 } { 15 }$ 
A)   $\frac { 11 } { 34 }$ 
B)    $\frac { 1 } { 2 }$ 
C)    $\frac { 23 } { 34 }$ 
D)    $\frac { 11 } { 15 }$ 
E)    $\frac { 4 } { 15 }$

Question 11

Student admissions are based on the following table, which shows the profile, by Math SAT I scores, of admitted students at some university for the Fall 2004 semester. Determine the theoretical probability of the event: "An applicant who had a Math SAT below 400 was admitted." (Round your answer to the nearest 0.01). $$\begin{array} { | l | l | l | l | l | l | l | } 
\hline & \mathbf { 2 0 0 } - \mathbf { 3 9 9 } & \mathbf { 4 0 0 } - \mathbf { 4 9 9 } & \mathbf { 5 0 0 } - \mathbf { 5 9 9 } & \mathbf { 6 0 0 } - \mathbf { 6 9 9 } & \mathbf { 7 0 0 } - \mathbf { 8 0 0 } & \text { Total } \
\hline \text { Admitted } & 6 & 212 & 1,137 & 2,882 & 5,293 & 9,530 \
\hline \begin{array} { l } 
\text { Not } \
\text { Admitted }
\end{array} & 734 & 3,517 & 9,211 & 12,230 & 5,150 & 30,842 \
\hline \begin{array} { l } 
\text { Total } \
\text { Applicants }
\end{array} & 740 & 3,729 & 10,348 & 15,112 & 10,443 & 40,372 \
\hline
\end{array}$$ ​
Enter your answer in decimal form, not as a fraction.
The probability is __________.

Accepted Answer

The answer of Student admissions are based on the following...

Question 12

A bag contains 3 red marbles, 2 green ones, 1 fluorescent pink one, 2 yellow ones, and 2 orange ones. Suzy grabs 4 at random. Find the probability of the event: "She gets all the red ones, given that she gets the yellow one."

Accepted Answer

A)  $\frac { 5 } { 28 }$ 
B)  $\frac { 1 } { 21 }$ 
C)  $\frac { 5 } { 21 }$ 
D)  $\frac { 1 } { 84 }$ 
E)  $\frac { 5 } { 84 }$ 
A)  $\frac { 5 } { 28 }$ 
B)  $\frac { 1 } { 21 }$ 
C)  $\frac { 5 } { 21 }$ 
D)  $\frac { 1 } { 84 }$ 
E)  $\frac { 5 } { 84 }$

Question 13

The table shows the results of a survey of 99 authors by a publishing company. Compute the conditional probability: An author is established, given that she is successful. $$\begin{array} { | l | l | l | l | } 
\hline & \text { New Authors } & \begin{array} { l } 
\text { Established } \
\text { Authors }
\end{array} & \text { Total } \
\hline \text { Successful } & 5 & 26 & 31 \
\hline \text { Unsuccessful } & 14 & 54 & 68 \
\hline \text { Total } & 19 & 80 & 99 \
\hline
\end{array}$$

Accepted Answer

A)  $\frac { 25 } { 33 }$ 
B)  $\frac { 5 } { 31 }$ 
C)  $\frac { 3 } { 13 }$ 
D)  $\frac { 26 } { 31 }$ 
E)  $\frac { 26 } { 99 }$ 
A)  $\frac { 25 } { 33 }$ 
B)  $\frac { 5 } { 31 }$ 
C)  $\frac { 3 } { 13 }$ 
D)  $\frac { 26 } { 31 }$ 
E)  $\frac { 26 } { 99 }$

Question 14

According to a study conducted by the Harvard School of Public Health, a driver who was not wearing a seatbelt was 84% more likely to be killed in an accident if the car had an air bag that deployed than if it did not. Airbags deployed in 25% of all accidents. For a driver not wearing a seatbelt, what is the probability that the airbag deployed in an accident in which the driver was killed

Accepted Answer

A) 0.21 
B)  0.38 
C)  0.62 
D)  0.72 
E)  0.28 
A) 0.21 
B)  0.38 
C)  0.62 
D)  0.72 
E)  0.28

Question 15

According to the New York Times/CBS poll of March, 2005, 75% agreed that it should be the government's responsibility to provide a decent standard of living for the elderly, and 44% agreed that it would be a good idea to invest part of their Social Security taxes on their own. What is the smallest percentage of people who could have agreed with both statements  What is the largest percentage of people who could have agreed with both statements  ?

Accepted Answer

A) The smallest percentage is 20%, the largest percentage is 100%. 
B)  The smallest percentage is 19%, the largest percentage is 31%. 
C)  The smallest percentage is 19%, the largest percentage is 44%. 
D)  The smallest percentage is 14%, the largest percentage is 99%. 
E)  The smallest percentage is 21%, the largest percentage is 44%. 
A) The smallest percentage is 20%, the largest percentage is 100%. 
B)  The smallest percentage is 19%, the largest percentage is 31%. 
C)  The smallest percentage is 19%, the largest percentage is 44%. 
D)  The smallest percentage is 14%, the largest percentage is 99%. 
E)  The smallest percentage is 21%, the largest percentage is 44%.

Question 16

The Sorry State Lottery requires you to select 5 different numbers drawn at random from a set numbered 1 to 43. (Order is not important.) You are a Big Winner if the 5 numbers you select agree with those in the drawing.  
What is the probability of being a Big Winner

Accepted Answer

A)  $\frac { 1 } { 70,221,789 }$ 
B)  $\frac { 1 } { 75,335,902 }$ 
C)  $\frac { 1 } { 38,470,009 }$ 
D)  $\frac { 1 } { 962,598 }$ 
E)  $\frac { 1 } { 28,460,833 }$ 
A)  $\frac { 1 } { 70,221,789 }$ 
B)  $\frac { 1 } { 75,335,902 }$ 
C)  $\frac { 1 } { 38,470,009 }$ 
D)  $\frac { 1 } { 962,598 }$ 
E)  $\frac { 1 } { 28,460,833 }$

Question 17

A bag contains 4 red marbles, 3 green ones, 3 white ones, and 1 purple one. Michelle reaches into the bag and grabs 5 of the marbles. Find the probability that she has 2 green ones and 1 of each of the other colors.

Accepted Answer

A)   $\frac { 6 } { 77 }$ 
B)    $\frac { 1 } { 14 }$ 
C)    $\frac { 1 } { 12 }$ 
D)    $\frac { 5 } { 28 }$ 
E)    $\frac { 3 } { 11 }$ 
A)   $\frac { 6 } { 77 }$ 
B)    $\frac { 1 } { 14 }$ 
C)    $\frac { 1 } { 12 }$ 
D)    $\frac { 5 } { 28 }$ 
E)    $\frac { 3 } { 11 }$

Question 18

The following table shows the results of a survey of authors by a (fictitious) publishing company: $$\begin{array} { | l | l | l | l | } 
\hline & \text { New Authors } & \begin{array} { l } 
\text { Established } \
\text { Authors }
\end{array} & \text { Total } \
\hline \text { Successful } & 5 & 25 & 30 \
\hline \text { Unsuccessful } & 15 & 55 & 70 \
\hline \text { Total } & 20 & 80 & 100 \
\hline
\end{array}$$   Consider the following events:
S: An author is successful; U: An author is unsuccessful; N: An author is new; and E: An author is established.
Which of the following pairs of events are mutually exclusive:

Accepted Answer

A) U and E 
B)  both S and N, and U and E 
C)  U and S 
D)  S and N 
E)  none 
A) U and E 
B)  both S and N, and U and E 
C)  U and S 
D)  S and N 
E)  none

Question 19

If a coin is tossed 6 times, find the probability of the sequence H, T, T, H, H, H.

Accepted Answer

The answer of If a coin is tossed 6 times,...

Question 20

If $A \cap B = \varnothing$ , $P ( B ) = 0.1$ , and $P ( A \cup B ) = 0.1$ , then find $P ( A )$ .
​ $P ( A ) =$ __________

Accepted Answer

The answer of If $A \cap B = \varnothing$ ,...

In a London State daily lottery, a sequence of 3 (not necessarily different) digits in the range 0-7 are selected at random. Find the probability that 2 of 3 digits are the same.

A pair of dice is cast, and the number that appears uppermost on each die is observed. Find the probability of the event that the sum of the numbers is 9.

Compute the following quantities. $P ( A \cap C )$ , $P ( A \cap D )$ , $P ( B \cap C )$ , and $P ( B \cap D )$ $Compute the following quantities. P ( A \cap C ) , P ( A \cap D ) , P ( B \cap C ) , and P ( B \cap D )$

The table shows the results of a survey of 100 authors by a publishing company. Compute the conditional probability: An author is established, given that she is successful. New Authors Established Authors Total Successful 5 26 31 Unsuccessful 14 55 69 Total 19 81 100

A bag contains 3 red marbles, 2 green ones, 1 fluorescent pink one, 2 yellow ones, and 2 orange ones. Suzy grabs 4 at random. Find the probability of the event: "She gets all the red ones, given that she gets the yellow one."

The table shows the results of a survey of 99 authors by a publishing company. Compute the conditional probability: An author is established, given that she is successful. New Authors Established Authors Total Successful 5 26 31 Unsuccessful 14 54 68 Total 19 80 99

The Sorry State Lottery requires you to select 5 different numbers drawn at random from a set numbered 1 to 43. (Order is not important.) You are a Big Winner if the 5 numbers you select agree with those in the drawing. What is the probability of being a Big Winner

A bag contains 4 red marbles, 3 green ones, 3 white ones, and 1 purple one. Michelle reaches into the bag and grabs 5 of the marbles. Find the probability that she has 2 green ones and 1 of each of the other colors.

If a coin is tossed 6 times, find the probability of the sequence H, T, T, H, H, H.

If $A \cap B = \varnothing$ , $P ( B ) = 0.1$ , and $P ( A \cup B ) = 0.1$ , then find $P ( A )$ . $P ( A ) =$ __________

Functions and Applications

Nonlinear Functions and Models

The Mathematics of Finance

Systems of Linear Equations and Matrices

Matrix Algebra and Applications

Linear Programming

Sets and Counting

Random Variables and Statistics

Introduction to the Derivative

Techniques of Differentiation

Applications of the Derivative

The Integral

Further Integration Techniques and Applications of the Integral

Functions of Several Variables

Trigonometric Models

Filters

Exam 8: Probability

In a London State daily lottery, a sequence of 3 (not necessarily different) digits in the range 0-7 are selected at random. Find the probability that 2 of 3 digits are the same.

A pair of dice is cast, and the number that appears uppermost on each die is observed. ​ Find the probability of the event that the sum of the numbers is 9.

Compute the following quantities. P(A∩C)P ( A \cap C )P(A∩C) , P(A∩D)P ( A \cap D )P(A∩D) , P(B∩C)P ( B \cap C )P(B∩C) , and P(B∩D)P ( B \cap D )P(B∩D)

The table shows the results of a survey of 100 authors by a publishing company. Compute the conditional probability: An author is established, given that she is successful. New Authors Established Authors Total Successful 5 26 31 Unsuccessful 14 55 69 Total 19 81 100

A bag contains 3 red marbles, 2 green ones, 1 fluorescent pink one, 2 yellow ones, and 2 orange ones. Suzy grabs 4 at random. Find the probability of the event: "She gets all the red ones, given that she gets the yellow one."

The table shows the results of a survey of 99 authors by a publishing company. Compute the conditional probability: An author is established, given that she is successful. New Authors Established Authors Total Successful 5 26 31 Unsuccessful 14 54 68 Total 19 80 99

The Sorry State Lottery requires you to select 5 different numbers drawn at random from a set numbered 1 to 43. (Order is not important.) You are a Big Winner if the 5 numbers you select agree with those in the drawing. What is the probability of being a Big Winner

A bag contains 4 red marbles, 3 green ones, 3 white ones, and 1 purple one. Michelle reaches into the bag and grabs 5 of the marbles. Find the probability that she has 2 green ones and 1 of each of the other colors.

If a coin is tossed 6 times, find the probability of the sequence H, T, T, H, H, H.

If A∩B=∅A \cap B = \varnothingA∩B=∅ , P(B)=0.1P ( B ) = 0.1P(B)=0.1 , and P(A∪B)=0.1P ( A \cup B ) = 0.1P(A∪B)=0.1 , then find P(A)P ( A )P(A) . ​ P(A)=P ( A ) =P(A)= __________

Functions and Applications

Nonlinear Functions and Models

The Mathematics of Finance

Systems of Linear Equations and Matrices

Matrix Algebra and Applications

Linear Programming

Sets and Counting

Random Variables and Statistics

Introduction to the Derivative

Techniques of Differentiation

Applications of the Derivative

The Integral

Further Integration Techniques and Applications of the Integral

Functions of Several Variables

Trigonometric Models

Filters

A pair of dice is cast, and the number that appears uppermost on each die is observed. Find the probability of the event that the sum of the numbers is 9.

Compute the following quantities. $P ( A \cap C )$ , $P ( A \cap D )$ , $P ( B \cap C )$ , and $P ( B \cap D )$ $Compute the following quantities. P ( A \cap C ) , P ( A \cap D ) , P ( B \cap C ) , and P ( B \cap D )$

If $A \cap B = \varnothing$ , $P ( B ) = 0.1$ , and $P ( A \cup B ) = 0.1$ , then find $P ( A )$ . $P ( A ) =$ __________