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

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

Q: Given events $$A$$ and $$B$$ are not disjoint, which formula correctly calculates $$P(A \text{ or } B)$$?

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

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

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

Q: Which of the following is the correct formula for the conditional probability of $$B$$ given $$A$$?

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

Question 1

Suppose you toss a fair coin three times. What is the probability of getting exactly two heads?

Accepted Answer

$$\frac{3}{8}$$

Question 2

Which of the following statements about the sample space $$S is $$TRUE?

Accepted Answer

The sample space $$S$$ contains all possible outcomes of a random experiment.

Question 3

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

Accepted Answer

$$0.9$$

Question 4

A family has two children. Let $$A be $$the event that the first child is a boy, and $$B be $$the event that the second child is a boy. Are $$A$$ and $$B$$ disjoint?

Accepted Answer

No, because both events can occur together.

Question 5

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

Accepted Answer

$$P(A^c) = 1 - P(A)$$

Question 6

In a college, 65% of students own a car, 82% own a computer, and 55% own both. What is the probability that a randomly chosen student owns neither a car nor a computer?

Accepted Answer

$$0.08$$

Question 7

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

Accepted Answer

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

Question 8

You draw two cards from a deck with replacement. Let $$A be $$the event that the first card is a spade, and $$B be $$the event that the second card is a five. Are $$A$$ and $$B$$ independent?

Accepted Answer

Yes, because the cards are drawn with replacement.

Question 9

Suppose you toss a coin twice. Let $$A be $$the event that the first toss is a head, and $$B be $$the event that the second toss is a tail. Are $$A$$ and $$B$$ independent?

Accepted Answer

Yes, because the outcome of one toss does not affect the other.

Question 10

Given events $$A$$ and $$B$$ are not disjoint, which formula correctly calculates $$P(A 	ext{ or } B)$$?

Accepted Answer

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

Question 11

A statistics class has 80 students: 35 domestic and 45 international. If you choose a student at random, what is the probability that the student is international or lives in Vancouver, given that 24 international students live in Vancouver and 18 domestic students live in Vancouver?

Accepted Answer

$$\frac{67}{80}$$

Question 12

Which of the following is NOT a property of probability $$P(A)$$?

Accepted Answer

$$P(A) \u003e 1 is $$possible for some events

Question 13

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

Accepted Answer

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

Question 14

You choose 2 students at random without replacement from a class with 10 students living in Richmond and 13 living in Burnaby or Coquitlam. What is the probability that one student lives in Richmond and one lives in Burnaby or Coquitlam?

Accepted Answer

$$\frac{260}{6320}$$

Question 15

If you choose 3 students at random with replacement from a class where 45 out of 80 are international students, what is the probability that at least one of the chosen students is international?

Accepted Answer

$$1 - \left(\frac{35}{80}\$$right)^3$$

Question 16

Which of the following is the correct formula for the conditional probability of $$B$$ given $$A$$?

Accepted Answer

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

Question 17

If you roll a fair die, what is the probability of rolling an even number or a number greater than 4?

Accepted Answer

$$\frac{4}{6}$$

Question 18

Which of the following is a necessary condition for two events $$A$$ and $$B to be $$independent?

Accepted Answer

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

Question 19

A student is randomly chosen from a statistics class. Let $$I be $$the event that the student is international, and $$B be $$the event that the student lives in Burnaby or Coquitlam. Are $$I$$ and $$B$$ independent if $$P(I) = \frac{45}{80}$$, $$P(B) = \frac{13}{80}$$, and $$P(I 	ext{ and } B) = \frac{6}{80}$$?

Accepted Answer

No, because $$P(I 	ext{ and } B) 
eq P(I) 	imes P(B)$$

Probability Concepts and Rules: Chapters 11 & 12 Study Notes

스터디 가이드 - 연습 문제

학습 가이드 - 플래시카드