Question 1

Use a graphing calculator to develop a simulation of the given problem (100 trials). Describe the simulation, then
estimate the probability based on its results.
-The probability that when 75 people are surveyed, at least five of them have the same birth date. (Ignore leap years).

Accepted Answer

The answer of Use a graphing calculator to develop a...

Question 2

Solve the problem.
-8 basketball players are to be selected to play in a special game. The players will be selected from a list of 27 players. If the players are selected randomly, what is the probability that the 8 tallest players will be selected? 
A) $\frac { 8 } { 27 }$
B) $\frac { 1 } { 40,320 }$
C) $\frac { 1 } { 2,220,075 }$
D) $\frac { 1 } { 213,127,200 }$

Accepted Answer

The probability of selecting the 8 tallest players is the number of favorable outcomes (1 way to select the 8 tallest) divided by the total number of ways to select 8 players from 27, which is $\binom{27}{8}$. This equals $\frac{1}{2,220,075}$.

Question 3

Use a graphing calculator to develop a simulation of the given problem (100 trials). Describe the simulation, then
estimate the probability based on its results.
-Assume that ten percent of us are left-handed. The probability of getting at least two left-handed people in a group of 7.

Accepted Answer

The answer of Use a graphing calculator to develop a...

Question 4

Solve the problem.
-A state lottery involves the random selection of six different numbers between 1 and 29. If you select one six number combination, what is the probability that it will be the winning combination? 
A) $\frac { 1 } { 720 }$
B) $\frac { 1 } { 594,823,321 }$
C) $\frac { 1 } { 342,014,400 }$
D) $\frac { 1 } { 475,020 }$

Accepted Answer

The total number of combinations of 6 numbers from 29 is given by the combination formula $\binom{29}{6}$, which equals 475,020. The probability of selecting the winning combination is $\frac{1}{475,020}$.

Question 5

Evaluate the expression.
-$${ } _ { 5 } \mathrm { P } _ { 4 }$$
A)5
B)24
C)1
D)120

Accepted Answer

$${ } _ { 5 } \mathrm { P } _ { 4 } = \frac{5!}{(5-4)!} = \frac{5 \times 4 \times 3 \times 2 \times 1}{1} = 120.$$

Question 6

Evaluate the expression.
-${ } _ { 8 } \mathrm { P } _ { 4 }$
A)2
B)1680
C)70
D)4

Accepted Answer

${ } _ { 8 } \mathrm { P } _ { 4 } = \frac{8!}{(8-4)!} = \frac{8 \times 7 \times 6 \times 5 \times 4!}{4!} = 8 \times 7 \times 6 \times 5 = 1680.$

Question 7

Use a graphing calculator to develop a simulation of the given problem (100 trials). Describe the simulation, then
estimate the probability based on its results.
-The probability of getting a total of 15 when four dice are thrown.

Accepted Answer

The answer of Use a graphing calculator to develop a...

Question 8

Use a graphing calculator to develop a simulation of the given problem (100 trials). Describe the simulation, then
estimate the probability based on its results.
-The probability of getting exactly three girls in a family of five children.

Accepted Answer

The answer of Use a graphing calculator to develop a...

Question 9

Evaluate the expression.
-${ } _ { 10 } \mathrm { C } _ { 2 }$
A) 5
B) 80,640
C) 40,320
D) 45

Accepted Answer

${ } _ { 10 } \mathrm { C } _ { 2 }$ calculates the number of combinations of 10 items taken 2 at a time, which is $\frac{10!}{2!(10-2)!} = \frac{10 \times 9}{2} = 45$.

Question 10

Solve the problem.
-The library is to be given 3 books as a gift. The books will be selected from a list of 18 titles. If each book selected must have a different title, how many possible selections are there?
A)4896
B)1.067062284e+15
C)816
D)6.402373706e+15

Accepted Answer

The number of ways to select 3 books from 18, with no repetition, is calculated using the combination formula: $C(n, k) = \frac{n!}{k!(n-k)!}$, where $n$ is the total number of items (18 books), and $k$ is the number of items to choose (3 books). Thus, $C(18, 3) = \frac{18!}{3!(18-3)!} = \frac{18 \times 17 \times 16}{3 \times 2 \times 1} = 816$.

Question 11

Solve the problem.
-There are 8 members on a board of directors. If they must form a subcommittee of 5 members, how many different subcommittees are possible?
A)6720
B)56
C)32,768
D)120

Accepted Answer

The number of ways to choose 5 members out of 8 for a subcommittee is calculated using the combination formula, which is C(n, k) = n! / [k!(n-k)!], where n is the total number of items, and k is the number of items to choose. Here, n=8 and k=5, so C(8, 5) = 8! / [5!(8-5)!] = 8! / (5!3!) = (8*7*6) / (3*2*1) = 56.

Question 12

Solve the problem.
-How many 5-digit numbers can be formed using the digits 1, 2, 3, 4, 5, 6, 7 if repetition of digits is not allowed?
A)2520
B)16,807
C)120
D)119

Accepted Answer

Since repetition of digits is not allowed, the first digit can be chosen in 7 ways (from 1 to 7), the second digit in 6 ways (remaining digits after the first is chosen), the third in 5 ways, the fourth in 4 ways, and the fifth in 3 ways. Multiplying these together gives the total number of possible numbers: 7 * 6 * 5 * 4 * 3 = 2520.

Question 13

Evaluate the expression.
-$5 ^ { P ^ { P _ { 4 } } }$
A) 0
B) 1
C) 15
D) 120

Accepted Answer

The answer of Evaluate the expression.
-\(5 ^ { P ^...

Question 14

Solve the problem.
-The organizer of a television show must select 5 people to participate in the show. The participants will be selected from a list of 26 people who have written in to the show. If the participants are selected randomly, what is the probability that the 5 youngest people will be selected? 
A) $\frac { 4 } { 13 }$
B) $\frac { 1 } { 7,893,600 }$
C) $\frac { 1 } { 120 }$
D) $\frac { 1 } { 65,780 }$

Accepted Answer

The probability is calculated using combinations. The total number of ways to select 5 people out of 26 is $C(26, 5)$. There is only 1 way to select the 5 youngest out of the 26. Thus, the probability is $\frac{1}{C(26, 5)} = \frac{1}{65,780}$.

Question 15

Evaluate the expression.
-${ } _ { 10 } \mathrm { P } _ { 4 }$
A) 5040
B) 6
C) 210
D) 34

Accepted Answer

${ } _ { 10 } \mathrm { P } _ { 4 } = \frac{10!}{(10-4)!} = \frac{10 \times 9 \times 8 \times 7 \times 6!}{6!} = 10 \times 9 \times 8 \times 7 = 5040.$

Question 16

Solve the problem.
-How many ways can 6 people be chosen and arranged in a straight line if there are 8 people to choose from?
A)20,160
B)720
C)40,320
D)48

Accepted Answer

There are 8 choices for the first person, 7 choices for the second person, 6 choices for the third person, and so on. So, the total number of ways is 8 * 7 * 6 * 5 * 4 * 3 = 20,160.

Question 17

Evaluate the expression.
-$$\frac { 10 ! } { 4 ! }$$
A) $\frac { 5 } { 2 }$
B) 2 !
C) 151,200
D) 40,000

Accepted Answer

The expression $\frac{10!}{4!}$ simplifies to $10 \times 9 \times 8 \times 7 \times 6 \times 5 = 151,200$, since $4!$ (which equals $4 \times 3 \times 2 \times 1 = 24$) cancels out the corresponding factors in $10!$.

Question 18

Evaluate the expression.
-$$2 !$$
A)0
B)1
C)2
D)4

Accepted Answer

The factorial of 2, denoted as $2!$, is calculated as $2 \times 1 = 2$.

Question 19

Use a graphing calculator to develop a simulation of the given problem (100 trials). Describe the simulation, then
estimate the probability based on its results.
-The probability of getting at least two boys in a family of seven children.

Accepted Answer

The answer of Use a graphing calculator to develop a...

Question 20

Solve the problem.
-How many ways can an IRS auditor select 4 of 10 tax returns for an audit?
A)10,000
B)24
C)210
D)5040

Accepted Answer

The number of ways to select 4 out of 10 tax returns is calculated using the combination formula, which is C(n, k) = n! / [k!(n-k)!], where n is the total number of items, k is the number of items to choose, and "!" denotes factorial. Here, n=10 and k=4, so C(10, 4) = 10! / [4!(10-4)!] = 10! / (4!6!) = (10*9*8*7) / (4*3*2*1) = 210.

Quiz 4: Probability

Use a graphing calculator to develop a simulation of the given problem (100 trials). Describe the simulation, then estimate the probability based on its results. -The probability that when 75 people are surveyed, at least five of them have the same birth date. (Ignore leap years).

Solve the problem. -8 basketball players are to be selected to play in a special game. The players will be selected from a list of 27 players. If the players are selected randomly, what is the probability that the 8 tallest players will be selected?

Use a graphing calculator to develop a simulation of the given problem (100 trials). Describe the simulation, then estimate the probability based on its results. -Assume that ten percent of us are left-handed. The probability of getting at least two left-handed people in a group of 7.

Solve the problem. -A state lottery involves the random selection of six different numbers between 1 and 29. If you select one six number combination, what is the probability that it will be the winning combination?

Evaluate the expression. - ${ } _ { 5 } \mathrm { P } _ { 4 }$

Evaluate the expression. - ${ } _ { 8 } \mathrm { P } _ { 4 }$

Use a graphing calculator to develop a simulation of the given problem (100 trials). Describe the simulation, then estimate the probability based on its results. -The probability of getting a total of 15 when four dice are thrown.

Use a graphing calculator to develop a simulation of the given problem (100 trials). Describe the simulation, then estimate the probability based on its results. -The probability of getting exactly three girls in a family of five children.

Evaluate the expression. - ${ } _ { 10 } \mathrm { C } _ { 2 }$

Solve the problem. -The library is to be given 3 books as a gift. The books will be selected from a list of 18 titles. If each book selected must have a different title, how many possible selections are there?

Solve the problem. -There are 8 members on a board of directors. If they must form a subcommittee of 5 members, how many different subcommittees are possible?

Solve the problem. -How many 5-digit numbers can be formed using the digits 1, 2, 3, 4, 5, 6, 7 if repetition of digits is not allowed?

Evaluate the expression. - $5 ^ { P ^ { P _ { 4 } } }$

Evaluate the expression. - ${ } _ { 10 } \mathrm { P } _ { 4 }$

Solve the problem. -How many ways can 6 people be chosen and arranged in a straight line if there are 8 people to choose from?

Evaluate the expression. - $\frac { 10 ! } { 4 ! }$

Evaluate the expression. - $2 !$

Use a graphing calculator to develop a simulation of the given problem (100 trials). Describe the simulation, then estimate the probability based on its results. -The probability of getting at least two boys in a family of seven children.

Solve the problem. -How many ways can an IRS auditor select 4 of 10 tax returns for an audit?

Quiz 4: Probability

Use a graphing calculator to develop a simulation of the given problem (100 trials). Describe the simulation, then estimate the probability based on its results. -The probability that when 75 people are surveyed, at least five of them have the same birth date. (Ignore leap years).

Solve the problem. -8 basketball players are to be selected to play in a special game. The players will be selected from a list of 27 players. If the players are selected randomly, what is the probability that the 8 tallest players will be selected?

Use a graphing calculator to develop a simulation of the given problem (100 trials). Describe the simulation, then estimate the probability based on its results. -Assume that ten percent of us are left-handed. The probability of getting at least two left-handed people in a group of 7.

Solve the problem. -A state lottery involves the random selection of six different numbers between 1 and 29. If you select one six number combination, what is the probability that it will be the winning combination?

Evaluate the expression. - 5P4{ } _ { 5 } \mathrm { P } _ { 4 }5​P4​

Evaluate the expression. - 8P4{ } _ { 8 } \mathrm { P } _ { 4 }8​P4​

Use a graphing calculator to develop a simulation of the given problem (100 trials). Describe the simulation, then estimate the probability based on its results. -The probability of getting a total of 15 when four dice are thrown.

Use a graphing calculator to develop a simulation of the given problem (100 trials). Describe the simulation, then estimate the probability based on its results. -The probability of getting exactly three girls in a family of five children.

Evaluate the expression. - 10C2{ } _ { 10 } \mathrm { C } _ { 2 }10​C2​

Solve the problem. -The library is to be given 3 books as a gift. The books will be selected from a list of 18 titles. If each book selected must have a different title, how many possible selections are there?

Solve the problem. -There are 8 members on a board of directors. If they must form a subcommittee of 5 members, how many different subcommittees are possible?

Solve the problem. -How many 5-digit numbers can be formed using the digits 1, 2, 3, 4, 5, 6, 7 if repetition of digits is not allowed?

Evaluate the expression. - 5PP45 ^ { P ^ { P _ { 4 } } }5PP4​

Evaluate the expression. - 10P4{ } _ { 10 } \mathrm { P } _ { 4 }10​P4​

Solve the problem. -How many ways can 6 people be chosen and arranged in a straight line if there are 8 people to choose from?

Evaluate the expression. - 10!4!\frac { 10 ! } { 4 ! }4!10!​

Evaluate the expression. - 2!2 !2!

Use a graphing calculator to develop a simulation of the given problem (100 trials). Describe the simulation, then estimate the probability based on its results. -The probability of getting at least two boys in a family of seven children.

Solve the problem. -How many ways can an IRS auditor select 4 of 10 tax returns for an audit?

Evaluate the expression. - ${ } _ { 5 } \mathrm { P } _ { 4 }$

Evaluate the expression. - ${ } _ { 8 } \mathrm { P } _ { 4 }$

Evaluate the expression. - ${ } _ { 10 } \mathrm { C } _ { 2 }$

Evaluate the expression. - $5 ^ { P ^ { P _ { 4 } } }$

Evaluate the expression. - ${ } _ { 10 } \mathrm { P } _ { 4 }$

Evaluate the expression. - $\frac { 10 ! } { 4 ! }$

Evaluate the expression. - $2 !$