No, because $$P(A|M) \neq P(A)$$

Question 1

Which of the following best describes the sample space for the experiment of tossing two fair coins, as shown in the tree diagram?

Accepted Answer

S = {(H, H), (H, T), (T, H), (T, T)}

Question 2

If an experiment consists of tossing five coins, how many possible experimental outcomes are there?

Accepted Answer

$$2^5 = 32$

Question 3

A parcel can follow 2 starting venues, use 3 cars, and reach 4 delivery points. How many different routes can the parcel take?

Accepted Answer

$$2 	imes 3 	imes 4 = 24$$

Question 4

Which formula is used to calculate the number of combinations of $$N$$ objects taken $$n at a $$time?

Accepted Answer

$$\frac{N!}{n!(N-n)!}$$

Question 5

In the context of probability, what does the shaded region in the Venn diagram for the union of two events $$A$$ and $$B$$ represent?

Accepted Answer

All sample points belonging to $$A or$$ $$B or $$both

Question 6

Given events $$A$$ and $$B$$, which equation correctly represents the addition law for probability?

Accepted Answer

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

Question 7

If two events $$A$$ and $$B$$ are mutually exclusive, what is $$P(A \cap B)$$?

Accepted Answer

$$0$$

Question 8

Which of the following is the correct formula for the conditional probability of $$A$$ given $$B$$?

Accepted Answer

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

Question 9

A quality control inspector selects 2 of 5 parts to inspect. How many arrangements may be selected if the order is important?

Accepted Answer

$$\frac{5!}{(5-2)!} = 20$$

Question 10

If the probability of seeing a lion is 0.3, what is the probability of not seeing a lion?

Accepted Answer

$$1 - 0.3 = 0.7$$

Question 11

Which law states that $$(A \cup B) = (B \cup A)$$ and $$(A \cap B) = (B \cap A)$$?

Accepted Answer

Commutative laws

Question 12

If $$P(A) = 0.4$$ and $$P(B) = 0.5$$, and $$A$$ and $$B$$ are independent, what is $$P(A \cap B)$$?

Accepted Answer

$$0.4 	imes 0.5 = 0.2$$

Question 13

Which method of assigning probabilities is most appropriate when all experimental outcomes are equally likely?

Accepted Answer

Classical method

Question 14

In a hospital study, the probability of 2 patients waiting for service at 9am is calculated as $$\frac{6}{20}. $$Which method is used?

Accepted Answer

Relative frequency method

Question 15

Which of the following is NOT a requirement for assigning probabilities?

Accepted Answer

Probabilities must be greater than 1

Question 16

If $$P(A) = 0.27$$ and $$P(A|M) = 0.3$$, are the events $$A$$ and $$M$$ independent?

Accepted Answer

No, because $$P(A|M) 
eq P(A)$$

Question 17

Which formula represents the multiplication law for the intersection of two events $$A$$ and $$B$$?

Accepted Answer

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

Question 18

Which of the following is a correct application of DeMorgan’s laws?

Accepted Answer

$$(A \cap B)^c = A^c \cup B^c$$

Question 19

A lottery game requires selecting 6 numbers from 49. How many possible combinations are there?

Accepted Answer

$$\frac{49!}{6!(49-6)!}$$

Introduction to Probability Theory: Experiments, Counting, and Probability Laws

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