Q: Which of the following is the correct formula for the classical probability of an event $$E$$?

$$\frac{\text{Number of ways } E \text{ can occur}}{\text{Total number of possible outcomes}}$$

Question 1

Which of the following best describes the sample space for the experiment: 'A commuter drives through a sequence of 3 intersections with traffic lights, each time either stopping (s) or continuing (c)'?

Accepted Answer

The set of all possible combinations of 's' and 'c' for three intersections: $$\{sss, ssc, scs, scc, css, csc, ccs, ccc\}$$

Question 2

A fair die is rolled. What is the probability of rolling an even number?

Accepted Answer

$$\frac{1}{2}$$

Question 3

In the context of probability, what is the complement of an event $$A$$?

Accepted Answer

The set of all outcomes that are not in $$A$$

Question 4

A company runs two types of promotions: 40% of customers received a discount coupon via email, 30% saw a promotional ad on social media, and 15% saw both. What is the probability that a randomly selected customer was exposed to at least one promotion?

Accepted Answer

$$0.40 + 0.30 - 0.15 = 0.55$$

Question 5

Which approach to assigning probabilities is based on expert opinion?

Accepted Answer

Subjective

Question 6

If two events $$A$$ and $$B$$ are mutually exclusive, which equation correctly represents the probability of their union?

Accepted Answer

$$P(A \cup B) = P(A) + P(B)$$

Question 7

In Ireland, 55% of the population have blood type O and 3% have blood type AB. What is the probability that a randomly selected person has blood type O or AB?

Accepted Answer

$$0.55 + 0.03 = 0.58$$

Question 8

What is the probability that a family with two children has at least one girl, assuming each child is equally likely to be a boy or a girl?

Accepted Answer

$$\frac{3}{4}$$

Question 9

Which formula represents the probability of the union of two events $$A$$ and $$B$$?

Accepted Answer

$$P(A \cup B) = P(A) + P(B) - P(A \cap B)$$

Question 10

A lottery requires matching 6 numbers from 47. What is the probability of winning with a single ticket?

Accepted Answer

$$\frac{1}{10,737,573}$$

Question 11

Which of the following is NOT a valid method for assigning probabilities?

Accepted Answer

Random assignment

Question 12

If $$P(A) = 0.7$$, what is the probability that event $$A$$ does NOT occur?

Accepted Answer

$$1 - 0.7 = 0.3$$

Question 13

Which statement about mutually exclusive events is correct?

Accepted Answer

They cannot occur together; $$A \cap B = \emptyset$$

Question 14

A video game is tested by 80 gamers, and 65 say it is playable. What is the relative frequency probability that the game is playable?

Accepted Answer

$$\frac{65}{80} = 0.8125$$

Question 15

Which of the following best describes an 'event' in probability theory?

Accepted Answer

A collection of one or more outcomes of an experiment

Question 16

If the probability of event $$A is$$ $$0.4$$ and the probability of event $$B is$$ $$0.5$$, and $$A$$ and $$B$$ are not mutually exclusive, and $$P(A \cap B) = 0.2$$, what is $$P(A \cup B)$$?

Accepted Answer

$$0.4 + 0.5 - 0.2 = 0.7$$

Question 17

Which of the following is the correct formula for the classical probability of an event $$E$$?

Accepted Answer

$$\frac{	ext{Number of ways } E 	ext{ can occur}}{	ext{Total number of possible outcomes}}$$

Question 18

If $$P(A) = 0.6$$ and $$P(A') is $$the probability of the complement of $$A$$, what is $$P(A')$$?

Accepted Answer

$$1 - 0.6 = 0.4$$

Question 19

Which of the following is an example of a subjective probability?

Accepted Answer

A doctor estimates the chance of recovery based on experience

Lecture 5: Probability – Foundations and Event Operations

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