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

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