Q: If $$P(A) = 0.3$$, $$P(B) = 0.4$$, and $$P(A \text{ and } B) = 0.12$$, are events $$A$$ and $$B$$ independent?

Yes, because $$0.3 \times 0.4 = 0.12$$

Q: A grocery store has 32 bags of chips, 9 of which are low salt. If you select two bags without replacement, what is the probability both are low salt?

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

Q: If a state license plate consists of three letters (excluding 'O') followed by four numbers (1–9), how many unique plates are possible?

$$25 \times 25 \times 25 \times 9 \times 9 \times 9 \times 9 = 102,515,625$$

Question 1

Which of the following best describes the sample space for the experiment of drawing a card from a standard deck?

Accepted Answer

All 52 cards in the deck

Question 2

A company has 16 discount cards: 10 cards for 15%, 3 for 20%, 2 for 25%, and 1 for 30%. What is the empirical probability that a randomly selected card will have a discount greater than 15%?

Accepted Answer

$$\frac{6}{16} = 0.375$$

Question 3

If $$P(A) = 0.3$$ and $$P(A') is $$the probability of the complement of $$A$$, what is $$P(A')$$?

Accepted Answer

$$0.7$$

Question 4

A contingency table shows that 17 first-year students are in-state, 12 are out-of-state, and there are 50 students in total. What is the probability that a randomly selected student is both a first-year student and in-state?

Accepted Answer

$$\frac{17}{50} = 0.34$$

Question 5

Which of the following is a property of mutually exclusive events?

Accepted Answer

They cannot occur at the same time.

Question 6

If $$P(A) = 0.4$$, $$P(B) = 0.5$$, and $$A$$ and $$B$$ are independent, what is $$P(A 	ext{ and } B)$$?

Accepted Answer

$$0.2$$

Question 7

A business manager estimates a 75% chance of a hiring freeze next year. This is an example of which type of probability?

Accepted Answer

Subjective probability

Question 8

A restaurant has 3 appetizers, 4 main courses, and 2 desserts. Using the fundamental counting principle, how many different meals can a customer order (one of each)?

Accepted Answer

$$3 	imes 4 	imes 2 = 24$$

Question 9

How many ways can 5 players be arranged in a line for a team photo?

Accepted Answer

$$5! = 120$$

Question 10

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

Accepted Answer

$$\frac{52!}{5!\,47!}$$

Question 11

If $$P(A) = 0.3$$, $$P(B) = 0.4$$, and $$P(A 	ext{ and } B) = 0.12$$, are events $$A$$ and $$B$$ independent?

Accepted Answer

Yes, because $$0.3 	imes 0.4 = 0.12$$

Question 12

A grocery store has 32 bags of chips, 9 of which are low salt. If you select two bags without replacement, what is the probability both are low salt?

Accepted Answer

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

Question 13

Given $$P(A) = 0.5$$, $$P(B) = 0.3$$, and $$P(A 	ext{ and } B) = 0.1$$, what is $$P(A 	ext{ or } B)$$?

Accepted Answer

$$0.5 + 0.3 - 0.1 = 0.7$$

Question 14

Which formula correctly expresses Bayes’ Theorem for two events $$A_1$$ and $$A_2$$?

Accepted Answer

$$P(A_1$|B) = \frac{P(A_1$)P(B|A_1$)}{P(A_1$)P(B|A_1$) + P(A_2$)P(B|A_2$)}$$

Question 15

A contingency table shows 70 satisfied customers who ordered meat, 100 satisfied who ordered fish, 10 not satisfied who ordered meat, and 20 not satisfied who ordered fish. What is the probability a randomly selected customer was satisfied given they ordered fish?

Accepted Answer

$$\frac{100}{120} = 0.833$$

Question 16

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

Accepted Answer

$$25 	imes 25 	imes 25 	imes 9 	imes 9 	imes 9 	imes 9 = 102,515,625$$

Question 17

Which of the following is NOT a basic property of probability?

Accepted Answer

The probability of any event can be negative.

Question 18

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

Accepted Answer

$$0.4 	imes 0.7 = 0.28$$

Question 19

Which of the following best describes the law of large numbers?

Accepted Answer

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

Chapter 4: Introduction to Probabilities – Business Statistics Study Notes

Guida di studio - Domande di pratica

Study guide - Flashcard