Q: A bag contains 9 low-salt and 23 regular potato chip bags. If you select two bags without replacement, what is the probability that both are low-salt?

$$\frac{9}{32} \times \frac{8}{31}$$

Q: Given the following probabilities: $$P(A) = 0.4$$, $$P(B) = 0.5$$, and $$P(A \text{ and } B) = 0.2. $$Are events A and B independent?

Yes, because $$0.4 \times 0.5 = 0.2$$

Question 1

A company inspects a batch of 100 products and finds that 8 are defective. What is the empirical probability that a randomly selected product from this batch is not defective?

Accepted Answer

$$\frac{92}{100}$$

Question 2

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

Accepted Answer

$$\frac{2}{6}$$

Question 3

A contingency table shows that 17 first-year students are in-state and 12 are out-of-state, out of a total of 29 first-year students. What is the probability that a randomly selected first-year student is in-state?

Accepted Answer

$$\frac{17}{29}$$

Question 4

Which of the following best describes mutually exclusive events?

Accepted Answer

Events that cannot occur at the same time

Question 5

A bag contains 9 low-salt and 23 regular potato chip bags. If you select two bags without replacement, what is the probability that both are low-salt?

Accepted Answer

$$\frac{9}{32} 	imes \frac{8}{31}$$

Question 6

If the probability of Event A is 0.3 and the probability of its complement is 0.7, which rule is being demonstrated?

Accepted Answer

Complement Rule

Question 7

A student is selected at random from a group of 50. The probability that the student is a junior and in-state is $$\frac{2}{50}. $$What is this type of probability called?

Accepted Answer

Joint probability

Question 8

Given the following probabilities: $$P(A) = 0.4$$, $$P(B) = 0.5$$, and $$P(A 	ext{ and } B) = 0.2. $$Are events A and B independent?

Accepted Answer

Yes, because $$0.4 	imes 0.5 = 0.2$$

Question 9

A restaurant offers 3 appetizers, 4 main courses, and 2 desserts. How many different three-course meals can be ordered?

Accepted Answer

$$3 	imes 4 	imes 2$$

Question 10

If a state license plate consists of 3 letters (excluding 'O') followed by 4 numbers (1-9), how many unique plates are possible?

Accepted Answer

$$25^3$$ 	imes $$9^4$$

Question 11

A poker hand consists of 5 cards drawn from a standard deck of 52 cards. How many different hands are possible?

Accepted Answer

$$\frac{52!}{5!(52-5)!}$$

Question 12

If $$P(A) = 0.3$$, $$P(B) = 0.4$$, and A and B are mutually exclusive, what is $$P(A 	ext{ or } B)$$?

Accepted Answer

$$0.7$$

Question 13

A student is satisfied with their meal (Event A) and ordered fish (Event D). If $$P(A 	ext{ and } D) = 0.50$$ and $$P(D) = 0.60$$, what is the conditional probability that a student is satisfied given they ordered fish?

Accepted Answer

$$\frac{0.50}{0.60}$$

Question 14

Which of the following is an example of subjective probability?

Accepted Answer

A manager estimates a 60% chance of a project being completed on time based on experience

Question 15

If $$P(A|B) = 0.7$$ and $$P(B) = 0.4$$, what is $$P(A 	ext{ and } B)$$?

Accepted Answer

$$0.28$$

Question 16

Bayes’ Theorem is used to:

Accepted Answer

Update the probability of an event based on new information

Question 17

If the probability of drawing a 15% discount card from Kohl’s is $$0.625$$, what is the probability of not drawing a 15% discount card?

Accepted Answer

$$0.375$$

Question 18

Which of the following statements is TRUE about independent and mutually exclusive events?

Accepted Answer

Two events cannot be both independent and mutually exclusive

Chapter 4: Introduction to Probabilities – Business Statistics Study Guide

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