Q: Which formula correctly represents the probability of the union of two disjoint events A and B?

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

Q: Which of the following is the correct formula for conditional probability?

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

Q: Which of the following is the General Addition Rule for any two events A and B?

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

Question 1

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

Accepted Answer

As the number of trials increases, the proportion of times an event occurs approaches its probability.

Question 2

A deck of cards contains 52 cards. What is the probability of drawing a face card (Jack, Queen, or King) from a standard deck?

Accepted Answer

$$\frac{12}{52}$$

Question 3

Which of the following is a legitimate probability assignment for a single event A?

Accepted Answer

$$0 \leq P(A) \leq 1$$

Question 4

If $$P(A) = 0.7$$, what is $$P(A^c)$$, the probability of the complement of A?

Accepted Answer

$$0.3$$

Question 5

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

Accepted Answer

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

Question 6

A survey finds that 33% of students are in a relationship, 25% are involved in sports, and 11% are in both. What is the probability that a randomly selected student is either in a relationship or involved in sports?

Accepted Answer

$$0.33 + 0.25 - 0.11 = 0.47$$

Question 7

Which of the following statements about disjoint and independent events is TRUE?

Accepted Answer

Disjoint events cannot be independent.

Question 8

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

Accepted Answer

$$\frac{0.2}{0.5} = 0.4$$

Question 9

If two events A and B are independent, which equation must be true?

Accepted Answer

$$P(A|B) = P(A)$$

Question 10

A factory produces toasters with a 15% defect rate. If you buy three toasters, what is the probability that at least one is NOT defective?

Accepted Answer

$$1 - 0.15 = 0.85$$

Question 11

Which of the following is the correct formula for conditional probability?

Accepted Answer

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

Question 12

In a contingency table, the probability of being a French speaker given that the person is from Quebec is:

Accepted Answer

$$\frac{50}{55}$$

Question 13

Which of the following is the General Addition Rule for any two events A and B?

Accepted Answer

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

Question 14

If $$P(B|A) = 0.3$$ and $$P(A) = 0.5$$, what is $$P(A 	ext{ and } B)$$?

Accepted Answer

$$0.5 	imes 0.3 = 0.15$$

Question 15

A tree diagram is most useful for:

Accepted Answer

Visualizing sequences of events and conditional probabilities.

Question 16

Which of the following is NOT a common mistake when working with probability?

Accepted Answer

Using the complement rule for independent events only.

Question 17

If $$P(A) = 0.6$$ and $$P(B) = 0.5$$, and A and B are independent, what is $$P(A 	ext{ and } B)$$?

Accepted Answer

$$0.6 	imes 0.5 = 0.3$$

Question 18

Which of the following best describes empirical probability?

Accepted Answer

Probability based on the long-run relative frequency of an event’s occurrence.

mar 16 Probability Rules and Applications in Statistics

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