Q: Which formula correctly represents the probability of the complement of event $$A$$?

$$P(\text{not } A) = 1 - P(A)$$

Q: If $$P(A) = 0.4$$ and $$P(B) = 0.5$$, and $$A$$ and $$B$$ are independent, what is $$P(A \text{ and } B)$$?

$$P(A \text{ and } B) = P(A) \times P(B) = 0.4 \times 0.5 = 0.2$$

Q: Which of the following is the correct formula for the probability of the union of two events $$A$$ and $$B$$?

$$P(A \text{ or } B) = P(A) + P(B) - P(A \text{ and } B)$$

Q: Which of the following is the correct formula for conditional probability $$P(A \mid B)$$?

$$P(A \mid B) = \frac{P(A \text{ and } B)}{P(B)}$$

Question 1

Which of the following best describes the Law of Large Numbers in probability?

Accepted Answer

As the number of trials increases, the empirical probability approaches the theoretical probability in the long run.

Question 2

Suppose you roll a fair six-sided die. What is the probability of rolling a number greater than 3?

Accepted Answer

$$\frac{3}{6} = 0.50$$

Question 3

If you flip a fair coin twice, what is the probability of getting exactly one head?

Accepted Answer

$$\frac{2}{4} = 0.5$$

Question 4

Given a standard deck of 52 cards, what is the probability of drawing a red card?

Accepted Answer

$$\frac{26}{52} = 0.5$$

Question 5

Which formula correctly represents the probability of the complement of event $$A$$?

Accepted Answer

$$P(	ext{not } A) = 1 - P(A)$$

Question 6

A survey of 831 people found 72 males with green eyes. What is the probability that a randomly selected person is both male and has green eyes?

Accepted Answer

$$\frac{28}{831} \approx 0.03$$

Question 7

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

Accepted Answer

$$P(A 	ext{ and } B) = P(A) 	imes P(B) = 0.4 	imes 0.5 = 0.2$$

Question 8

Which of the following is the correct formula for the probability of the union of two events $$A$$ and $$B$$?

Accepted Answer

$$P(A 	ext{ or } B) = P(A) + P(B) - P(A 	ext{ and } B)$$

Question 9

Suppose you roll a fair six-sided die. What is the probability of NOT rolling a 4?

Accepted Answer

$$\frac{5}{6} \approx 0.83$$

Question 10

In a study, 406 people are male and 72 people have green eyes. If 28 people are both male and have green eyes, what is the probability that a randomly selected person is male OR has green eyes?

Accepted Answer

$$\frac{406 + 72 - 28}{831} = \frac{450}{831} \approx 0.54$$

Question 11

If you roll a fair six-sided die, what is the probability of rolling an even number greater than 2?

Accepted Answer

$$\frac{2}{6} = 0.33$$

Question 12

Which of the following statements about independent events is TRUE?

Accepted Answer

The occurrence of one event does not affect the probability of the other event.

Question 13

Given $$P(A) = 0.3$$, what is $$P(	ext{not } A)$$?

Accepted Answer

$$1 - 0.3 = 0.7$$

Question 14

If you flip a fair coin three times, what is the probability of getting exactly two heads?

Accepted Answer

$$\frac{3}{8} = 0.375$$

Question 15

A table shows that 72 people have green eyes and 406 are male out of 831 total. What is the probability that a randomly selected person is green-eyed GIVEN they are male?

Accepted Answer

$$\frac{28}{406} \approx 0.07$$

Question 16

Which of the following is the correct formula for conditional probability $$P(A \mid B)$$?

Accepted Answer

$$P(A \mid B) = \frac{P(A 	ext{ and } B)}{P(B)}$$

Question 17

If you roll a fair six-sided die, what is the probability of rolling a number that is both even and greater than 2?

Accepted Answer

$$\frac{2}{6} = 0.33$$

Question 18

A study of 1,665 students found 83 had green eyes and were high school students. What is the probability that a randomly selected student is both green-eyed and a high school student?

Accepted Answer

$$\frac{83}{1,665} \approx 0.05$$

Question 19

If $$P(A) = 0.2$$ and $$P(B) = 0.3$$, and $$P(A 	ext{ and } B) = 0.1$$, what is $$P(A 	ext{ or } B)$$?

Accepted Answer

$$0.2 + 0.3 - 0.1 = 0.4$$

Fundamentals of Probability and Basic Statistics

Study Guide - Practice Questions

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