Q: If $A$ and $B$ are disjoint events, which formula correctly gives the probability that either $A$ or $B$ occurs?

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

Question 1

Which of the following best describes a random process as discussed in probability theory?

Accepted Answer

A process where individual outcomes are uncertain, but a regular distribution emerges over many repetitions.

Question 2

Given the sample space $S = \{1, 2, 3, 4, 5, 6\}$ for rolling a fair six-sided die, what is the probability of rolling an even number?

Accepted Answer

$\frac{1}{2}$

Question 3

If you flip a coin three times, which of the following is the correct sample space $S$?

Accepted Answer

$S = \{HHH, HHT, HTH, HTT, THH, THT, TTH, TTT\}$

Question 4

Which rule states that the probability of the complement of event $A$ is $1$ minus the probability of $A$?

Accepted Answer

Rule 4

Question 5

A die is rolled 5000 times and the number 5 appears 830 times. What is the empirical probability of rolling a 5?

Accepted Answer

$0.1666$

Question 6

Which of the following is NOT a valid probability rule?

Accepted Answer

The probability of any event can be negative.

Question 7

If $A$ and $B$ are disjoint events, which formula correctly gives the probability that either $A$ or $B$ occurs?

Accepted Answer

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

Question 8

Suppose the probability of an event $A$ is $0.3$. What is the probability that $A$ does NOT occur?

Accepted Answer

$0.7$

Question 9

Which of the following best describes the empirical approach to probability?

Accepted Answer

Estimating probability by repeating a process and counting the frequency of an event.

Question 10

If the probability of rating the economy as 'Excellent' is $0.03$, 'Good' is $0.12$, and 'Fair' is $0.25$, what is the probability of a positive ranking (Excellent, Good, or Fair)?

Accepted Answer

$0.40$

Question 11

Which of the following is a valid probability distribution for a random variable $X$ with possible values $0, 1, 2$?

Accepted Answer

$P(X=0)=0.2, P(X=1)=0.5, P(X=2)=0.3$

Question 12

A random variable $X$ is defined as the waiting time (in minutes) for a bus to arrive. Which of the following statements is true?

Accepted Answer

The value of $X$ can vary and is determined by a random process.

Question 13

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

Accepted Answer

$1$

Question 14

Which of the following is an example of an outcome in a random process?

Accepted Answer

Drawing the two of diamonds from a deck of cards.

Question 15

If the probability of rolling a 2 on a fair die is $\frac{1}{6}$, what is the probability of NOT rolling a 2?

Accepted Answer

$\frac{5}{6}$

Question 16

Which of the following best describes the sample space for tossing a coin twice?

Accepted Answer

$S = \{HH, HT, TH, TT\}$

Question 17

If $P(A) = 0.4$ and $P(B) = 0.3$, and $A$ and $B$ are disjoint, what is $P(A 	ext{ or } B)$?

Accepted Answer

$0.7$

Question 18

Which of the following is NOT a property of probability?

Accepted Answer

The probability of any event can exceed 1.

Question 19

A quality inspector rates four CD players as either 'acceptable' (A) or 'unacceptable' (U). How many possible outcomes are there for the sequence of ratings?

Accepted Answer

$16$

Probability and Random Variables: Foundations for Psychology

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