Q: Which of the following statements is TRUE regarding mutually exclusive events?

If events are mutually exclusive, $P(A \text{ and } B) = 0$.

Q: How many combinations are possible if you select 2 letters from A, B, C, D (order does not matter)?

$\frac{4!}{2! \times (4-2)!} = 6$

Q: A dean wants to schedule meetings with 5 out of 37 students who are falling behind. In how many different ways can she select the students if the order does not matter?

$\frac{37!}{5! \times (37-5)!}$

Question 1

A statistics class has 39 students, and 19 of them have unpaid temporary access to Pearson MyLab. What is the probability that a randomly selected student from the class has paid access?

Accepted Answer

$\frac{20}{39}$

Question 2

Which of the following best describes a 'simple event' in probability theory?

Accepted Answer

An event that cannot be simplified and consists of a single outcome.

Question 3

If you roll a fair six-sided die, what is the classical probability of rolling a number greater than 4?

Accepted Answer

$\frac{2}{6}$

Question 4

A survey of 400 graduates found that 102 had between $5,000-$9,999 in student loans. What is the empirical probability that a randomly selected graduate had loans in this range?

Accepted Answer

$\frac{102}{400}$

Question 5

Which method of assigning probability is most appropriate when you use intuition or experience to estimate the likelihood of an event?

Accepted Answer

Subjective probability

Question 6

If $P(A) = 0.7$, what is the probability of the complement of event A?

Accepted Answer

$0.3$

Question 7

In a contingency table, the probability of a student being both female and a freshman is $0.34$. The probability of being female is $0.58$, and the probability of being a freshman is $0.40$. What is the probability that a student is either female or a freshman?

Accepted Answer

$0.58 + 0.40 - 0.34 = 0.64$

Question 8

Which of the following statements is TRUE regarding mutually exclusive events?

Accepted Answer

If events are mutually exclusive, $P(A 	ext{ and } B) = 0$.

Question 9

Suppose the probability that it rains tomorrow is $0.3$, and the probability that you carry an umbrella given that it rains is $0.9$. What is the probability that it rains and you carry an umbrella?

Accepted Answer

$0.3 	imes 0.9 = 0.27$

Question 10

If events A and B are independent, which of the following is TRUE?

Accepted Answer

$P(A|B) = P(A)$

Question 11

A restaurant offers 3 types of entrée and 2 types of dessert. Using the fundamental counting principle, how many different meal combinations are possible?

Accepted Answer

$3 	imes 2 = 6$

Question 12

How many permutations are possible if you select and arrange 2 letters from A, B, C, D?

Accepted Answer

$4! / (4-2)! = 12$

Question 13

How many combinations are possible if you select 2 letters from A, B, C, D (order does not matter)?

Accepted Answer

$\frac{4!}{2! 	imes (4-2)!} = 6$

Question 14

A dean wants to schedule meetings with 5 out of 37 students who are falling behind. In how many different ways can she select the students if the order does not matter?

Accepted Answer

$\frac{37!}{5! 	imes (37-5)!}$

Question 15

Which of the following is an example of a subjective probability?

Accepted Answer

Estimating the probability that inflation will exceed 4% next year based on expert opinion.

Question 16

If the probability of Event A is $0.4$ and the probability of Event B is $0.5$, and they are mutually exclusive, what is the probability of A or B?

Accepted Answer

$0.4 + 0.5 = 0.9$

Question 17

Which statement about the law of large numbers is correct?

Accepted Answer

As the number of trials increases, the empirical probability approaches the classical probability.

Question 18

Given a contingency table, how do you convert frequencies to probabilities?

Accepted Answer

Divide each frequency by the total number of observations.

Question 19

If $P(A 	ext{ and } B) = 0.12$ and $P(B) = 0.4$, what is the conditional probability $P(A|B)$?

Accepted Answer

$\frac{0.12}{0.4} = 0.3$

Chapter 4: Introduction to Probabilities – Business Statistics Study Notes

Study Guide - Practice Questions

Study Guide - Flashcards