Q: If two events A and B are independent, which formula correctly expresses $$P(A \text{ AND } B)$$?

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

Q: If $$P(A) = 0.3$$, $$P(B) = 0.5$$, and $$P(A \text{ AND } B) = 0.15$$, are events A and B independent?

Yes, because $$0.3 \times 0.5 = 0.15$$

Question 1

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

Accepted Answer

It states that the empirical probability of an event will approach the theoretical probability as the number of trials increases.

Question 2

Given the table, what is the probability that a randomly selected person is a female who rides the bus?

Accepted Answer

$$ \frac{32}{278} $$

Question 3

If two events A and B are independent, which formula correctly expresses $$P(A 	ext{ AND } B)$$?

Accepted Answer

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

Question 4

What is the probability that a randomly selected person rides a bike, given that the person is male?

Accepted Answer

$$ \frac{14}{124} $$

Question 5

Which of the following statements about randomness is correct?

Accepted Answer

Randomness means that there is no predictable pattern and all outcomes are equally likely.

Question 6

Suppose you roll two fair six-sided dice. What is the probability that the sum is 7?

Accepted Answer

$$ \frac{1}{6} $$

Question 7

Which of the following is an example of empirical probability?

Accepted Answer

Observing that heads appeared 48 times in 100 coin flips.

Question 8

If 45% of Americans keep their social media accounts private, what is the probability that all 4 randomly selected Americans keep their accounts private?

Accepted Answer

$$ 0.45^4$ $$

Question 9

What is the probability that at least one of four randomly selected Americans keeps their social media accounts private, given that 45% keep their accounts private?

Accepted Answer

$$ 1 - 0.55^4$ $$

Question 10

Which of the following best describes mutually exclusive events?

Accepted Answer

Events that cannot both occur at the same time.

Question 11

Given the table, what is the probability that a randomly selected person is female or rides the bus?

Accepted Answer

$$ \frac{154 + 55 - 32}{278} $$

Question 12

Suppose you roll two fair six-sided dice. What is the probability that the first die is a 4 and the sum is 7?

Accepted Answer

$$ \frac{1}{36} $$

Question 13

If $$P(A) = 0.3$$, $$P(B) = 0.5$$, and $$P(A 	ext{ AND } B) = 0.15$$, are events A and B independent?

Accepted Answer

Yes, because $$0.3 	imes 0.5 = 0.15$$

Question 14

What is the probability that a randomly selected person is male and walks?

Accepted Answer

$$ \frac{12}{278} $$

Question 15

If $$P(A|B) = 0.2$$ and $$P(B) = 0.5$$, what is $$P(A 	ext{ AND } B)$$?

Accepted Answer

$$ 0.1 $$

Question 16

Which of the following is NOT a property of probability?

Accepted Answer

Probability values can be negative.

Question 17

If you observe five heads in a row when flipping a coin, what does the Law of Large Numbers say about the next five flips?

Accepted Answer

The next five flips are still random and independent.

Question 18

Given the table, what is the probability that a randomly selected person rides a bike?

Accepted Answer

$$ \frac{21}{278} $$

Question 19

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

Accepted Answer

$$ 0.7 $$

Chapter 5 Review: Modeling Variation with Probability

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