Question 1

In a hand of poker, a player is dealt 5 cards at random from a deck of 52. Below is a list of poker hands ranked in order from the highest to the lowest, along with a description and example of each hand. Use the table to answer the problem.   
What is the probability of being dealt a full house 
Round your answer to five decimal places.

Accepted Answer

The answer of In a hand of poker, a player...

Question 2

Suzy grabs four marbles from a bag containing three white marbles and five blue marbles. Find the probability that exactly three of the marbles are blue.
​
Enter your answer as a fraction in lowest terms.

Accepted Answer

The answer of Suzy grabs four marbles from a bag...

Question 3

A bag contains 4 red marbles, 3 green ones, 3 white ones, and 1 purple one. Michelle reaches into the bag and grabs 6 of the marbles. Find the probability that she does not have all green ones. Express your answer as a fraction in lowest terms.

Accepted Answer

The answer of A bag contains 4 red marbles, 3...

Question 4

In the New York State daily lottery game, a sequence of 6 (not necessarily different) digits in the range of 0-9 is selected at random.
​
Find the probability that all 6 are different.
​
If necessary, round your answer to four decimal places.
​
P = __________
​

Accepted Answer

The answer of In the New York State daily lottery...

Question 5

A bag contains 6 red marbles, 3 green ones, 2 white ones, and 1 purple one. Michelle reaches into the bag and grabs 5 of the marbles. Find the probability that she has at least 1 green marble. Express your answer as a fraction in lowest terms.

Accepted Answer

The answer of A bag contains 6 red marbles, 3...

Question 6

The phrase "Dogs of the Dow" refers to the stocks listed in the Dow with the highest dividend yield. This table shows the top ten stocks of the "Dogs in the Dow" list. If you selected four of these stocks at random, what is the probability that your selection included the company with the highest yield and excluded the company with the lowest yield  $$\begin{array} { | c | c | c | } 
\hline \text { Symbol } & \text { Company } & \text { Yield } \
\hline \text { SBC } & \begin{array} { c } 
\text { SBC } \
\text { Communications }
\end{array} & 5.48 \% \
\hline \text { GM } & \text { General Motors } & 5.48 \% \
\hline \text { MRK } & \text { Merck } & 5.42 \% \
\hline \text { MO } & \text { Altria } & 4.55 \% \
\hline \text { VZ } & \text { Verizon } & 4.32 \% \
\hline \text { JPM } & \text { JP Morgan Chase } & 3.68 \% \
\hline \text { C } & \text { Citigroup } & 3.64 \% \
\hline \text { PFE } & \text { Pfizer } & 3.12 \% \
\hline \text { DD } & \text { DuPont } & 2.96 \% \
\hline \text { GE } & \text { General Electric } & 2.46 \% \
\hline
\end{array}$$

Accepted Answer

The answer of The phrase "Dogs of the Dow" refers...

Question 7

In a Paris daily lottery, a sequence of 3 (not necessarily different) digits in the range 0-6 is selected at random. Find the probability that 2 of the 3 digits are the same.

Accepted Answer

The answer of In a Paris daily lottery, a sequence...

Question 8

Suppose that a monkey sits at the computer keyboard and randomly strikes the 26 letter keys and the space bar. Find the probability that its first 39 characters (including space bar) will be "To be or not to be that is the question" .  
A) $\frac { C ( 39,27 ) } { 39 ! }$
B) $\frac { C ( 39,27 ) } { 27 ^ { 39 } }$
C) $\frac { 1 } { 27 ^ { 39 } }$
D) $\frac { 39 } { 27 ^ { 38 } }$
E) $\frac { 1 } { 27 ^ { 38 } }$

Accepted Answer

The probability is calculated as the chance of hitting each specific character in the sequence correctly out of 27 possible characters (26 letters + space bar), which is $\frac{1}{27}$ for each character. Since there are 39 characters to match exactly, the probability is $\frac{1}{27^{39}}$.

Question 9

The phrase "Dogs of the Dow" refers to the stocks listed in the Dow with the highest dividend yield. This table shows the top ten stocks of the "Dogs of the Dow" list. If you selected two of these stocks at random, what is the probability that both the stocks in your selection had yields of 3.5% or more  $$\begin{array} { | c | c | c | } 
\hline \text { Symbol } & \text { Company } & \text { Yield } \
\hline \text { SBC } & \text { SBC Communications } & 5.48 \% \
\hline \text { GM } & \text { General Motors } & 5.48 \% \
\hline \text { MRK } & \text { Merck } & 5.42 \% \
\hline \text { MO } & \text { Altria } & 4.55 \% \
\hline \text { VZ } & \text { Verizon } & 4.32 \% \
\hline \text { JPM } & \text { JP Morgan Chase } & 3.78 \% \
\hline \text { C } & \text { Citigroup } & 3.64 \% \
\hline \text { PFE } & \text { Pfizer } & 3.12 \% \
\hline \text { DD } & \text { DuPont } & 2.98 \% \
\hline \text { GE } & \text { General Electric } & 2.46 \% \
\hline
\end{array}$$

Accepted Answer

The answer of The phrase "Dogs of the Dow" refers...

Question 10

This table shows the result of the Big Eight Conference for the 1990 college football season. This is referred to as a "perfect progression". Assuming the "Won" score for each team is chosen at random at range 0-7, Find the probability that the results is form a perfect progression. $$\begin{array} { | c | c | c | } 
\hline \text { Team } & \text { Won } & \text { Lost } \
\hline \text { Nebraska(NU) } & 7 & 0 \
\hline \text { Oklahoma(OU) } & 6 & 1 \
\hline \text { Oklahoma State(OSU) } & 5 & 2 \
\hline \text { Colorado(CU) } & 4 & 3 \
\hline \text { Iowa State(ISU) } & 3 & 4 \
\hline \text { Missouri(MU) } & 2 & 5 \
\hline \text { Kansas(KU) } & 1 & 6 \
\hline \text { Minnesota State(MSU) } & 0 & 7 \
\hline
\end{array}$$  
A) $\frac { 1 } { 8 ^ { 8 } }$
B) $\frac { 1 } { 8 }$
C) $\frac { 8 ! } { 8 ^ { 7 } }$
D) $\frac { 7 ! } { 7 ^ { 7 } }$
E) $\frac { 8 ! } { 8 ^ { 8 } }$

Accepted Answer

The probability is calculated by considering the number of ways to arrange the teams in a perfect progression (which is 1, since the progression is fixed) over the total number of ways to assign wins to the teams. Since each team can have a win total between 0 and 7 (inclusive), there are 8 possibilities for each of the 8 teams, leading to $8^8$ total combinations. Thus, the probability is $\frac{8!}{8^8}$, as 8! represents the number of ways to arrange 8 unique items.

Question 11

​A bag contains 6 red marbles, 3 green ones, 3 yellow ones, and 1 black one. Michelle reaches into the bag and grabs 4 of the marbles. Find the probability that she has 2 yellow ones and 1 black and 1 green one.
​

Accepted Answer

The answer of ​A bag contains 6 red marbles, 3...

Question 12

The graph consists of a collection of nodes (the dots in the figure) connected by edges (line segments from one node to another). A move on a graph is a move from one node to another along the single edge. Find the probability of moving from Start to Finish in a sequence of two random moves in the graph. (All directions are equally likely.)     
A) $\frac { 3 } { 16 }$
B) $\frac { 1 } { 4 }$
C) $\frac { 1 } { 16 }$
D) $\frac { 1 } { 8 }$
E) $\frac { 3 } { 8 }$

Accepted Answer

The answer of The graph consists of a collection of...

Question 13

The graph consists of a collection of nodes (the dots in the figure) connected by edges (line segments from one node to another). A move on a graph is a move from one node to another along the single edge. Find the probability of moving from Start to Finish in a sequence of two random moves in the graph. (All directions are equally likely.)
​

Accepted Answer

The answer of The graph consists of a collection of...

Question 14

Suppose that a monkey sits at the computer keyboard and randomly strikes the 26 letter keys and the space bar. Find the probability that its first 65 characters (including spaces) will be "All the world is a stage and all the men and women merely players."

Accepted Answer

The answer of Suppose that a monkey sits at the...

Question 15

Your company is considering offering 400 employees the opportunity to transfer to its new headquarters in Ottawa and, as personnel manager, you decide that it would be fairest if the transfer offers are decided by means of a lottery. Assuming that your company currently employs 50 managers, 50 factory workers, and 600 miscellaneous stuff, find the probability that all managers will be offered the opportunity and the probability that you will be offered the opportunity.  
A)The probability that all managers will be offered the opportunity is $\frac { C ( 650,350 ) } { C ( 700,400 ) }$ . The probability that you will be offered the opportunity is $\frac { C ( 649,349 ) } { C ( 700,400 ) }$ . 
B) The probability that all managers will be offered the opportunity is $\frac { C ( 700,350 ) } { C ( 700,400 ) }$ .
The probability that you will be offered the opportunity is $\frac { C ( 649,349 ) } { C ( 700,400 ) }$ .
C) The probability that all managers will be offered the opportunity is $\frac { C ( 650,350 ) } { C ( 700,400 ) }$ .
The probability that you will be offered the opportunity is $\frac { C ( 699,399 ) } { C ( 700,400 ) }$ . 
D) The probability that all managers will be offered the opportunity is $\frac { C ( 700,350 ) } { C ( 700,400 ) }$ .
The probability that you will be offered the opportunity is $\frac { C ( 699,399 ) } { C ( 700,400 ) }$ . 
E) The probability that all managers will be offered the opportunity is $\frac { C ( 650,400 ) } { C ( 700,350 ) }$ .
The probability that you will be offered the opportunity is $\frac { C ( 649,349 ) } { C ( 700,400 ) }$ .

Accepted Answer

The answer of Your company is considering offering 400 employees...

Question 16

This table shows the result of the Big Eight Conference for the 1990 college football season. This is referred to as a "perfect progression". Assuming the "Lost" score for each team is chosen at random at range 0-7, find the probability that the result is from a perfect progression. $$\begin{array} { | c | c | c | } 
\hline \text { Team } & \text { Won } & \text { Lost } \
\hline \text { Nebraska(NU) } & 7 & 0 \
\hline \text { Oklahoma(OU) } & 6 & 1 \
\hline \text { Oklahoma State(OSU) } & 5 & 2 \
\hline \text { Colorado(CU) } & 4 & 3 \
\hline \text { Iowa State(ISU) } & 3 & 4 \
\hline \text { Missouri(MU) } & 2 & 5 \
\hline \text { Kansas(KU) } & 1 & 6 \
\hline \text { Minnesota State(MSU) } & 0 & 7 \
\hline
\end{array}$$

Accepted Answer

The answer of This table shows the result of the...

Question 17

A bag contains 4 red marbles, 2 green ones, 4 white ones, and 1 purple one. Michelle reaches into the bag and grabs 6 of the marbles. Find the probability that she does not have all red ones. Express your answer as a fraction in the lowest terms.

Accepted Answer

The answer of A bag contains 4 red marbles, 2...

Question 18

A bag contains 4 red marbles, 4 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 red ones and 1 of each of the other colors. Express your answer as a fraction in lowest terms.

Accepted Answer

The answer of A bag contains 4 red marbles, 4...

Question 19

In a (fictitious) soccer tournament involving the four teams San Diego State, De Paul, Colgate, and Hofstra, find the probability that Hofstra will play De Paul in the finals and win. (Assume that all outcomes are equally likely and that the teams not listed in the first round slots are placed at random.)     
A) $\frac { 1 } { 8 }$
B) $\frac { 1 } { 2 }$
C) $\frac { 3 } { 8 }$
D) $\frac { 1 } { 16 }$
E) $\frac { 1 } { 4 }$

Accepted Answer

The answer of In a (fictitious) soccer tournament involving the...

Question 20

The Sorry State Lottery requires you to select 7 different numbers drawn at random from a set numbered 1 to 43. (Order is not important.) You are a Big Winner if the 7 numbers you select agree with those in the drawing.
 
What is the probability of being a Big Winner

Accepted Answer

The answer of The Sorry State Lottery requires you to...

Quiz 8: Probability

Suzy grabs four marbles from a bag containing three white marbles and five blue marbles. Find the probability that exactly three of the marbles are blue. Enter your answer as a fraction in lowest terms.

A bag contains 4 red marbles, 3 green ones, 3 white ones, and 1 purple one. Michelle reaches into the bag and grabs 6 of the marbles. Find the probability that she does not have all green ones. Express your answer as a fraction in lowest terms.

In the New York State daily lottery game, a sequence of 6 (not necessarily different) digits in the range of 0-9 is selected at random. Find the probability that all 6 are different. If necessary, round your answer to four decimal places. P = __________

A bag contains 6 red marbles, 3 green ones, 2 white ones, and 1 purple one. Michelle reaches into the bag and grabs 5 of the marbles. Find the probability that she has at least 1 green marble. Express your answer as a fraction in lowest terms.

In a Paris daily lottery, a sequence of 3 (not necessarily different) digits in the range 0-6 is selected at random. Find the probability that 2 of the 3 digits are the same.

Suppose that a monkey sits at the computer keyboard and randomly strikes the 26 letter keys and the space bar. Find the probability that its first 39 characters (including space bar) will be "To be or not to be that is the question" .

A bag contains 6 red marbles, 3 green ones, 3 yellow ones, and 1 black one. Michelle reaches into the bag and grabs 4 of the marbles. Find the probability that she has 2 yellow ones and 1 black and 1 green one.

Suppose that a monkey sits at the computer keyboard and randomly strikes the 26 letter keys and the space bar. Find the probability that its first 65 characters (including spaces) will be "All the world is a stage and all the men and women merely players."

A bag contains 4 red marbles, 2 green ones, 4 white ones, and 1 purple one. Michelle reaches into the bag and grabs 6 of the marbles. Find the probability that she does not have all red ones. Express your answer as a fraction in the lowest terms.

A bag contains 4 red marbles, 4 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 red ones and 1 of each of the other colors. Express your answer as a fraction in lowest terms.

The Sorry State Lottery requires you to select 7 different numbers drawn at random from a set numbered 1 to 43. (Order is not important.) You are a Big Winner if the 7 numbers you select agree with those in the drawing. What is the probability of being a Big Winner

Quiz 8: Probability

Suzy grabs four marbles from a bag containing three white marbles and five blue marbles. Find the probability that exactly three of the marbles are blue. ​ Enter your answer as a fraction in lowest terms.

A bag contains 4 red marbles, 3 green ones, 3 white ones, and 1 purple one. Michelle reaches into the bag and grabs 6 of the marbles. Find the probability that she does not have all green ones. Express your answer as a fraction in lowest terms.

In the New York State daily lottery game, a sequence of 6 (not necessarily different) digits in the range of 0-9 is selected at random. ​ Find the probability that all 6 are different. ​ If necessary, round your answer to four decimal places. ​ P = __________ ​

A bag contains 6 red marbles, 3 green ones, 2 white ones, and 1 purple one. Michelle reaches into the bag and grabs 5 of the marbles. Find the probability that she has at least 1 green marble. Express your answer as a fraction in lowest terms.

In a Paris daily lottery, a sequence of 3 (not necessarily different) digits in the range 0-6 is selected at random. Find the probability that 2 of the 3 digits are the same.

Suppose that a monkey sits at the computer keyboard and randomly strikes the 26 letter keys and the space bar. Find the probability that its first 39 characters (including space bar) will be "To be or not to be that is the question" .

​A bag contains 6 red marbles, 3 green ones, 3 yellow ones, and 1 black one. Michelle reaches into the bag and grabs 4 of the marbles. Find the probability that she has 2 yellow ones and 1 black and 1 green one. ​

Suppose that a monkey sits at the computer keyboard and randomly strikes the 26 letter keys and the space bar. Find the probability that its first 65 characters (including spaces) will be "All the world is a stage and all the men and women merely players."

A bag contains 4 red marbles, 2 green ones, 4 white ones, and 1 purple one. Michelle reaches into the bag and grabs 6 of the marbles. Find the probability that she does not have all red ones. Express your answer as a fraction in the lowest terms.

A bag contains 4 red marbles, 4 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 red ones and 1 of each of the other colors. Express your answer as a fraction in lowest terms.

The Sorry State Lottery requires you to select 7 different numbers drawn at random from a set numbered 1 to 43. (Order is not important.) You are a Big Winner if the 7 numbers you select agree with those in the drawing. What is the probability of being a Big Winner

Suzy grabs four marbles from a bag containing three white marbles and five blue marbles. Find the probability that exactly three of the marbles are blue. Enter your answer as a fraction in lowest terms.

In the New York State daily lottery game, a sequence of 6 (not necessarily different) digits in the range of 0-9 is selected at random. Find the probability that all 6 are different. If necessary, round your answer to four decimal places. P = __________

A bag contains 6 red marbles, 3 green ones, 3 yellow ones, and 1 black one. Michelle reaches into the bag and grabs 4 of the marbles. Find the probability that she has 2 yellow ones and 1 black and 1 green one.