Q: Which formula correctly expresses the probability of the union of two events $$A$$ and $$B (i.e$$., $$P(A \text{ or } B)) $$using the general addition rule?

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

Question 1

Suppose you roll a fair six-sided die. What is the probability of rolling an odd number?

Accepted Answer

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

Question 2

A card is drawn at random from a standard deck of 52 cards. Let event $$A be$$ 'drawing a heart' and event $$B be$$ 'drawing a face card.' Are events $$A$$ and $$B$$ mutually exclusive?

Accepted Answer

No, because there are face cards that are also hearts.

Question 3

If $$P(E) = 0.7$$, what is $$P(	ext{not } E)$$?

Accepted Answer

$$0.3$$

Question 4

In a university, 554 students are from the U.S., 314 from Canada, and 125 from Mexico, out of 11,544 students. What is the probability that a randomly selected student is from the U.S. or Canada?

Accepted Answer

$$\frac{554 + 314}{11,544}$$

Question 5

Which of the following best describes the complement of the event 'at least 50 students are business majors'?

Accepted Answer

Fewer than 50 students are business majors.

Question 6

If two events $$A$$ and $$B$$ are mutually exclusive, what is $$P(A 	ext{ and } B)$$?

Accepted Answer

$$0$$

Question 7

A contingency table shows that there are 170 associate professors in their thirties at a university. If there are 1,164 faculty members in total, what is the probability that a randomly selected faculty member is an associate professor in their thirties?

Accepted Answer

$$\frac{170}{1,164}$$

Question 8

Which formula correctly expresses the probability of the union of two events $$A$$ and $$B (i.e$$., $$P(A 	ext{ or } B)) $$using the general addition rule?

Accepted Answer

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

Question 9

In a lottery, a 4-digit number is chosen at random from 0000 to 9999. What is the probability that all four digits are the same?

Accepted Answer

$$\frac{10}{10,000}$$

Question 10

Given the contingency table, what is the probability that a randomly selected faculty member is either under 30 or an instructor?

Accepted Answer

$$\frac{68}{1,164} + \frac{33}{1,164} - \frac{6}{1,164}$$

Question 11

If $$P(A) = 0.4$$, $$P(B) = 0.5$$, and $$P(A 	ext{ and } B) = 0.2$$, what is $$P(A 	ext{ or } B)$$?

Accepted Answer

$$0.4 + 0.5 - 0.2 = 0.7$$

Question 12

Which of the following is NOT a property of probability?

Accepted Answer

The probability of any event is always greater than 1.

Question 13

A faculty member is selected at random. What is the probability that the member is a full professor aged 40–49?

Accepted Answer

$$\frac{156}{1,164}$$

Question 14

If $$P(A) = 0.3$$ and $$P(	ext{not } A) = 0.7$$, which rule is being used?

Accepted Answer

The Complementation Rule

Question 15

Which of the following best describes mutually exclusive events?

Accepted Answer

Events that cannot occur at the same time.

Question 16

If the probability that a car sold is a small car is $$0.40$$, what is the probability that a car sold is not a small car?

Accepted Answer

$$1 - 0.40 = 0.60$$

Probability Concepts and Rules: Structured Study Notes

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