Question 1

Which formula represents the number of combinations (unordered sets) of $$r$$ objects chosen from $$n$$ distinct objects?

Accepted Answer

$$\frac{n!}{r!(n-r)!}$$

Question 2

A box contains ping pong balls as shown: 2 yellow 5s, 1 black 5, 1 black 10, 1 yellow 15, 1 black 20. What is the probability of selecting a yellow ball given the ball shows a '5'?

Accepted Answer

$$\frac{2}{3}$$

Question 3

Given the car satisfaction table, what is the probability that a randomly selected person is satisfied with their car?

Accepted Answer

$$\frac{175}{250}$$

Question 4

From the movie preference table, what is the probability that a person prefers action movies given they are male?

Accepted Answer

$$\frac{25}{39}$$

Question 5

A survey of 350 students shows 17 sophomores live in apartments out of 47 total apartment residents. What is the probability that a student is a sophomore if the student lives in an apartment?

Accepted Answer

$$\frac{17}{47}$$

Question 6

How many different ways can you arrange 3 out of 16 billiard balls in order?

Accepted Answer

$$16 	imes 15 	imes 14$$

Question 7

If you roll a die 3 times, how many possible ordered outcomes are there?

Accepted Answer

$$6^3$$

Question 8

A standard deck of cards is shown. What is the probability of drawing a King given that the card is red?

Accepted Answer

$$\frac{2}{26}$$

Question 9

If the probability that it does not rain in Arizona in June is $$0.22$$, what is the probability that it rains at least once in June?

Accepted Answer

$$1 - 0.22 = 0.78$$

Question 10

How many different ways can you choose 3 books from a list of 5 books?

Accepted Answer

$$\frac{5!}{3!2!}$$

Question 11

A group of 100 people bought either a mobile phone or a tablet from brands A or B. If 30 people bought a mobile phone from brand B, what is the probability that a randomly selected person bought a mobile phone given they bought brand B?

Accepted Answer

$$\frac{30}{70}$$

Question 12

If you have 2 choices for an appetizer and 3 choices for a main course, how many different meal options do you have if you choose one of each?

Accepted Answer

$$2 	imes 3 = 6$$

Question 13

If a family of five is having portraits taken, how many ways can the family line up for the portrait?

Accepted Answer

$$5!$$

Question 14

A professor is creating an exam of 9 questions from a test bank of 12 questions. How many ways can she select and arrange the questions?

Accepted Answer

$$\frac{12!}{(12-9)!}$$

Question 15

Which of the following best describes a permutation?

Accepted Answer

An arrangement of objects where order matters

Question 16

If you select 3 digits from 10 marbles numbered 0 to 9, without replacement, how many different ordered numbers can you form?

Accepted Answer

$$10 	imes 9 	imes 8$$

Question 17

If an event with $$n$$ outcomes occurs $$r$$ times with repetition allowed, what is the number of ordered arrangements?

Accepted Answer

$$n^r$$

Question 18

A sundae bar has 6 toppings. If you can choose any number of toppings, how many different sundaes are possible?

Accepted Answer

$$2^6$$

Introductory Statistics Study Guide: Probability, Counting, and Conditional Probability

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