Q: Which of the following statements is TRUE about independent events?

If two events are independent, $$P(E \text{ and } F) = P(E) \cdot P(F)$$

Q: A CD has 13 tracks, and you like 5 of them. If two songs are played at random, what is the probability you like both?

$$\frac{5}{13} \times \frac{4}{12}$$

Question 1

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

Accepted Answer

The long-term relative frequency of an event approaches its theoretical probability as the number of trials increases.

Question 2

A bag contains 9 brown, 6 yellow, 7 red, 4 orange, 2 blue, and 2 green M&Ms. What is the probability that a randomly selected candy is not brown? Express your answer as a fraction in lowest terms.

Accepted Answer

$$\frac{6+7+4+2+2}{30} = \frac{21}{30}$$

Question 3

If the probability of an event $$E is$$ $$0.2$$, what is the probability of the complement of $$E$$?

Accepted Answer

$$0.8$$

Question 4

Suppose you roll two fair six-sided dice. What is the probability that the sum is greater than 10?

Accepted Answer

$$\frac{6}{36}$$

Question 5

A weather forecaster says there is a 30% chance of snow tomorrow. This probability is best described as:

Accepted Answer

Subjective probability

Question 6

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

Accepted Answer

$$0.7$$

Question 7

A standard deck of 52 cards is shuffled. What is the probability of drawing a queen or a diamond?

Accepted Answer

$$\frac{4}{52} + \frac{13}{52} - \frac{1}{52} = \frac{16}{52}$$

Question 8

Which of the following statements is TRUE about independent events?

Accepted Answer

If two events are independent, $$P(E 	ext{ and } F) = P(E) \cdot P(F)$$

Question 9

A basketball player makes 65% of his free throws. What is the probability he makes 8 in a row, assuming independence?

Accepted Answer

$$0.65^8$$

Question 10

Suppose the probability that a bulb will last 2 years is $$0.995. $$What is the probability that in a string of 100 bulbs, all 100 will last 2 years?

Accepted Answer

$$0.995^{100}$$

Question 11

Suppose 18% of a population is math phobic. If two people are randomly selected, what is the probability that at least one is math phobic?

Accepted Answer

$$1 - (1-0.18)^2$

Question 12

If $$P(E) = 0.11$$, $$P(T) = 0.08$$, and $$P(E 	ext{ and } T) = 0.03$$, what is $$P(E 	ext{ or } T)$$?

Accepted Answer

$$0.11 + 0.08 - 0.03 = 0.16$$

Question 13

A CD has 13 tracks, and you like 5 of them. If two songs are played at random, what is the probability you like both?

Accepted Answer

$$\frac{5}{13} 	imes \frac{4}{12}$$

Question 14

According to Benford’s Law, what is the probability that a randomly selected first digit is at least 6?

Accepted Answer

$$0.067 + 0.058 + 0.051 + 0.046$$

Question 15

A driver who is speeding has a probability of 0.8 of being pulled over, and a probability of 0.9 of getting a ticket if pulled over. What is the probability a speeding driver gets pulled over and gets a ticket?

Accepted Answer

$$0.8 	imes 0.9 = 0.72$$

Question 16

If two events $$E$$ and $$F$$ are independent, which of the following is always true?

Accepted Answer

$$P(E|F) = P(E)$$

Question 17

A sample of 150 residents was asked if they favor a zoning change. 80 in the city favor, 40 in the city oppose, 20 outside the city favor, and 10 outside the city oppose. What is $$P(	ext{favor}|	ext{in city})$$?

Accepted Answer

$$\frac{80}{120}$$

Chapter 5: Probability Rules and Applications – Study Notes

Guida di studio - Domande di pratica

Study guide - Flashcard