Q: If you roll a fair six-sided die, what is the probability of getting an odd number?

$$P(\text{odd}) = \frac{3}{6}$$

Question 1

Which of the following best describes a random process in statistics?

Accepted Answer

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

Question 2

Suppose you flip a coin three times. What is the sample space $$S$$ for this experiment?

Accepted Answer

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

Question 3

If you roll a fair six-sided die, what is the probability of getting an odd number?

Accepted Answer

$$P(	ext{odd}) = \frac{3}{6}$$

Question 4

Which rule states that the probability of the sample space $$S is $$always 1?

Accepted Answer

Rule 2

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

$$P(5) = \frac{830}{5000}$$

Question 6

If event $$A is$$ 'rolling an even number' on a die and event $$B is$$ 'rolling an odd number', what is $$P(A 	ext{ or } B)$$?

Accepted Answer

$$P(A 	ext{ or } B) = 1$$

Question 7

Which of the following is NOT a valid probability rule?

Accepted Answer

The probability of any event $$A$$ can be greater than 1.

Question 8

If $$P(A) = 0.5$$, what is the probability that event $$A$$ does NOT occur?

Accepted Answer

$$P(A') = 0.5$$

Question 9

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

Question 10

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

Accepted Answer

Estimating probability by repeating a process and counting the number of times an event occurs.

Question 11

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

Accepted Answer

$$P(A 	ext{ or } B) = 0.7$$

Question 12

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 13

A bus arrives at a stop at random times. Let $$X be $$the waiting time for the next bus. Which type of variable is $$X$$?

Accepted Answer

A random variable

Question 14

If the probability of an event $$A is$$ $$0$$, what does this mean?

Accepted Answer

Event $$A$$ can never occur.

Question 15

Suppose the probability of a positive economic ranking is the sum of the probabilities of 'Excellent', 'Good', and 'Fair'. If $$P(	ext{Excellent}) = 0.03$$, $$P(	ext{Good}) = 0.12$$, and $$P(	ext{Fair}) = 0.25$$, what is the probability of a positive ranking?

Accepted Answer

$$P(	ext{positive}) = 0.40$$

Question 16

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

Accepted Answer

Rolling a 4 on a die

Question 17

If $$P(A) = 0.6$$ and $$P(B) = 0.3$$ and $$A$$ and $$B$$ are disjoint, what is $$P(A 	ext{ or } B)$$?

Accepted Answer

$$P(A 	ext{ or } B) = 0.9$$

Question 18

Which statement about random variables is correct?

Accepted Answer

A random variable assigns a numerical value to each outcome of a random process.

Probability and Random Variables: Foundations and Rules

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