Question 1

Which of the following best describes a subjective probability?

Accepted Answer

A probability representing someone's personal degree of belief.

Question 2

Suppose you roll a fair six-sided die. What is the theoretical probability of rolling a number greater than 4?

Accepted Answer

$$\frac{1}{3}$$

Question 3

If $$P(A) = 0.4$$ and $$P(B) = 0.5$$, and A and B are disjoint events, what is $$P(A \cup B)$$?

Accepted Answer

$$0.9$$

Question 4

Which of the following statements about disjoint (mutually exclusive) events is TRUE?

Accepted Answer

If A and B are disjoint, then $$P(A \cap B) = 0.$$

Question 5

A legitimate probability assignment must satisfy which of the following conditions?

Accepted Answer

Each probability is between 0 and 1, and the sum of all probabilities is 1.

Question 6

If the probability of an event A occurring is $$0.7$$, what is the probability that A does NOT occur?

Accepted Answer

$$0.3$$

Question 7

Suppose events A and B are independent, with $$P(A) = 0.6$$ and $$P(B) = 0.5. $$What is $$P(A \cap B)$$?

Accepted Answer

$$0.3$$

Question 8

Which rule would you use to find the probability that at least one of two disjoint events occurs?

Accepted Answer

Addition Rule

Question 9

A bag contains 3 red balls and 7 blue balls. If you randomly select one ball, what is the probability it is not red?

Accepted Answer

$$0.7$$

Question 10

If $$P(A) = 0.2$$ and $$P(B) = 0.5$$, and A and B are independent, what is $$P(A \cap B)$$?

Accepted Answer

$$0.1$$

Question 11

A medical test for a disease has a 95% chance of correctly identifying a diseased patient (true positive) and a 5% chance of incorrectly identifying a healthy patient as diseased (false positive). If 1% of the population has the disease, what type of probability is being described by the 95% value?

Accepted Answer

Probability assignment rule

Question 12

If $$P(A) = 0.4$$, $$P(B) = 0.3$$, and A and B are disjoint, what is $$P(A \cup B)$$?

Accepted Answer

$$0.7$$

Question 13

Which of the following is NOT a requirement for a legitimate probability assignment?

Accepted Answer

Probabilities can be negative as long as the sum is 1.

Question 14

If the probability of event A is $$0.8$$, what is the probability of the complement of A?

Accepted Answer

$$0.2$$

Question 15

A weather forecaster says there is a 60% chance of rain tomorrow. This is an example of:

Accepted Answer

Subjective probability

Question 16

If two events are independent, which of the following is always true?

Accepted Answer

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

Question 17

A coin is flipped twice. What is the probability of getting at least one head?

Accepted Answer

$$0.75$$

Question 18

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

Accepted Answer

$$0.2$$

Question 19

Which of the following best describes the complement rule?

Accepted Answer

The probability of an event occurring is 1 minus the probability that it does not occur.

Question 20

A student assigns probabilities to the outcomes of rolling a die as follows: 1: 0.1, 2: 0.2, 3: 0.1, 4: 0.2, 5: 0.2, 6: 0.2. Is this a legitimate probability assignment?

Accepted Answer

No, because the sum of the probabilities is not 1.

Fundamental Probability Concepts and Rules

Guida di studio - Domande di pratica

Study guide - Flashcard