Resources

Resources

Bytelearn - cat image with glasses

AI tutor

Welcome to Bytelearn!

Let’s check out your problem:

Nia is 1 of 24 students in a class. Every month, Nia's teacher randomly selects 4 students from their class to act as class president, vice president, secretary, and treasurer. No one student can hold two positions.
In a given month, what is the probability that Nia is chosen as president?
Choose 1 answer:
(A)
(1)/(_(24)P_(4))
(B)
(1)/(_(24)C_(4))
(C)
(_(23)P_(3))/(_(24)P_(4))
(D)
((_(24)P_(1))*(_(24)P_(3)))/(_(24)P_(4))

Nia is $1$ of $24$ students in a class. Every month, Nia's teacher randomly selects $4$ students from their class to act as class president, vice president, secretary, and treasurer. No one student can hold two positions. $\newline$ In a given month, what is the probability that Nia is chosen as president? $\newline$ Choose $1$ answer: $\newline$ (A) $\frac{1}{{ }_{24} \mathrm{P}_{4}}$ $\newline$ (B) $\frac{1}{{ }_{24} \mathrm{C}_{4}}$ $\newline$ (C) $\frac{{ }_{23} \mathrm{P}_{3}}{{ }_{24} \mathrm{P}_{4}}$ $\newline$ (D) $\frac{\left({ }_{24} \mathbf{P}_{1}\right) \cdot\left({ }_{24} \mathrm{P}_{3}\right)}{{ }_{24} \mathrm{P}_{4}}$

View step-by-step help

View step-by-step help

Probability of simple events

Full solution

Q. Nia is

1

of

24

students in a class. Every month, Nia's teacher randomly selects

4

students from their class to act as class president, vice president, secretary, and treasurer. No one student can hold two positions.

\newline

In a given month, what is the probability that Nia is chosen as president?

\newline

Choose

1

answer:

\newline

(A)

\frac{1}{{ }_{24} \mathrm{P}_{4}}

\newline

(B)

\frac{1}{{ }_{24} \mathrm{C}_{4}}

\newline

(C)

\frac{{ }_{23} \mathrm{P}_{3}}{{ }_{24} \mathrm{P}_{4}}

\newline

(D)

\frac{\left({ }_{24} \mathbf{P}_{1}\right) \cdot\left({ }_{24} \mathrm{P}_{3}\right)}{{ }_{24} \mathrm{P}_{4}}

Understand the problem: Understand the problem. $\newline$ We need to calculate the probability that Nia is chosen as president out of $24$ students, with $4$ students being chosen for different positions.
Determine total combinations: Determine the total number of ways to choose $4$ students out of $24$ without regard to order. $\newline$ This is a combination problem because the order in which the students are chosen does not matter. We use the combination formula: $\newline$ $\binom{24}{4} = \frac{24!}{4! \times (24 - 4)!}$
Calculate combinations: Calculate the total number of combinations. $\newline$ $_{24}C_{4} = \frac{24!}{4! \times 20!}$ $\newline$ $_{24}C_{4} = \frac{(24 \times 23 \times 22 \times 21)}{(4 \times 3 \times 2 \times 1)}$ $\newline$ $_{24}C_{4} = 10626$
Determine probability: Determine the probability that Nia is chosen as president. $\newline$ Since there is only one president, and Nia has an equal chance of being chosen as any other student, the probability is simply $1$ out of the total number of combinations. $\newline$ $P(\text{Nia is president}) = \frac{1}{\binom{24}{4}}$
Substitute into formula: Substitute the total number of combinations into the probability formula. $\newline$ $P(\text{Nia is president}) = \frac{1}{10626}$
Choose correct answer: Choose the correct answer from the given options. $\newline$ The correct answer is (B) because it represents the probability of choosing Nia as president out of the total number of combinations of $4$ students from $24$ .

More problems from Probability of simple events

Question

6

-sided die two times. What is the probability of rolling a number greater than \(3\) and then rolling a number less than \(4\)? Write your answer as a percentage. ____ `%`

Posted 1 month ago

Question

9

college students running for student government class president. The candidates include

7

education majors.

\newline

6

of the candidates are randomly chosen to give the first

6

speeches, what is the probability that all of them are education majors?

\newline

Write your answer as a decimal rounded to four decimal places.

Posted 2 months ago

Question

In an experiment, the probability that event

A

\frac{2}{7}

, the probability that event

B

\frac{7}{9}

, and the probability that events

A

B

\frac{1}{9}

\newline

A

B

independent events?

\newline

\newline

\text{yes}

\newline

\text{no}

Posted 2 months ago

Question

At a science museum, visitors can compete to see who has a faster reaction time. Competitors watch a red screen, and the moment they see it turn from red to green, they push a button. The machine records their reaction times and also asks competitors to report their gender.

\newline

The probability that a competitor reacted in over

0.7

0.6

, the probability that a competitor was female is

0.4

, and the probability that a competitor reacted in over

0.7

seconds and was female is

0.3

\newline

What is the probability that a randomly chosen competitor reacted in over

0.7

seconds or was female?

\newline

Write your answer as a whole number, decimal, or simplified fraction.

\newline

Posted 2 months ago

Question

A restaurant server claims that \(28\)% of the time he leaves candy with the bill, the customer tips well.

\newline

If the server's claim is true, and one day he leaves candy with \(4\) customers' bills, what is the probability that exactly \(3\) of those customers will tip well?

\newline

Write your answer as a decimal rounded to the nearest thousandth.

Posted 1 month ago

Question

There is a spinner with `50` equally likely sections, numbered from `1` to `50`. You have the opportunity to spin it. If the number is odd, you win $`11`. If the number is even, you win nothing. If you play the game, what is the expected payoff?\(\$\)_____

Posted 2 months ago

Question

There are two different raffles you can enter.

\newline

In raffle A, one ticket will win a `$720` prize, and the other tickets will win nothing. There are

1,000

in the raffle, each costing `$11`.

\newline

Raffle B is for a `$370` prize. Out of

125

tickets, each costing `$5`, one ticket will win the prize, and the other tickets will win nothing.

\newline

Which raffle is a better deal?

\newline

\newline

\text{[A]Raffle A}

\newline

\text{[B]Raffle B}

Posted 2 months ago

Question

X

is a normally distributed random variable with mean

49

and standard deviation

25

\newline

What is the probability that

X

24

74

?

\newline

0.68-0.95-0.997

rule and write your answer as a decimal. Round to the nearest thousandth if necessary.

\newline

Posted 2 months ago

Question

X

is a normally distributed random variable with mean

65

and standard deviation

8

\newline

What is the probability that

X

62

68

?

\newline

Write your answer as a decimal rounded to the nearest thousandth.

\newline

Posted 2 months ago

Question

Complete the statement. Round your answer to the nearest thousandth.

\newline

In a population that is normally distributed with mean

43

and standard deviation

3

30\%

of the values are those less than ______.

Posted 2 months ago