Question 1

Which of the following best describes the sample space $$\Omega in $$probability theory?

Accepted Answer

The set of all possible outcomes of an experiment.

Question 2

Given two events $$A$$ and $$B$$ that are mutually exclusive, which formula correctly calculates $$P(A \cup B)$$?

Accepted Answer

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

Question 3

If $$P(A) = 0.3$$, $$P(B) = 0.5$$, and $$P(A \cap B) = 0.1$$, what is $$P(A \cup B)$$?

Accepted Answer

$$0.7$$

Question 4

Which of the following statements about conditional probability is correct?

Accepted Answer

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

Question 5

In a contingency table, what does a joint probability represent?

Accepted Answer

The probability that two events both occur.

Question 6

If $$P(A|B) = P(A)$$, what does this imply about events $$A$$ and $$B$$?

Accepted Answer

Events $$A$$ and $$B$$ are independent.

Question 7

Given the following table, what is $$P($$Purchased $$|$$ Planned$$)$$?

| Planned | Purchased | Not Purchased | Total |
|---------|-----------|---------------|-------|
| Yes     | 200       | 50            | 250   |
| No      | 100       | 650           | 750   |
| Total   | 300       | 700           | 1000  |

Accepted Answer

$$\dfrac{200}{250}$$

Question 8

Which of the following is the correct general addition rule for two events $$A$$ and $$B$$?

Accepted Answer

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

Question 9

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

Accepted Answer

$$0.2$$

Question 10

A company finds that $$P($$Employee stays$$) = 0.7$$ and $$P($$Employee leaves$$) = 0.3. If $$these are the only two possible outcomes, what property of probability does this illustrate?

Accepted Answer

Collectively exhaustive events

Question 11

Which formula correctly expresses the multiplication rule for independent events $$A$$ and $$B$$?

Accepted Answer

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

Question 12

In the context of a decision tree for probability, what does each branch represent?

Accepted Answer

A possible outcome and its associated probability.

Question 13

If $$P(A|B) = 0.6$$ and $$P(B) = 0.2$$, what is $$P(A \cap B)$$?

Accepted Answer

$$0.12$$

Question 14

Which of the following best describes marginal probability in a contingency table?

Accepted Answer

The probability of a single event occurring, regardless of other events.

Question 15

Given mutually exclusive and collectively exhaustive events $$B_1$$, $$B_2$$, ..., B_k$$, which formula gives the marginal probability for event A$?

Accepted Answer

$$P(A) = P(A|B_1$)P(B_1$) + P(A|B_2$)P(B_2$) + \cdots + P(A|B_k)P(B_k)$$

Fundamental Probability Concepts and Rules: Study Notes for Introductory Statistics

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