Question 1

Which of the following best describes the Law of Large Numbers?

Accepted Answer

As the number of trials increases, the relative frequency of an event approaches its theoretical probability.

Question 2

A batter believes he is 'due for a hit' after several misses. Which statistical misconception is he demonstrating?

Accepted Answer

The Nonexistent Law of Averages

Question 3

If you toss a coin and roll a die, what is the total number of possible outcomes?

Accepted Answer

$$2 	imes 6 = 12$$

Question 4

Which of the following probability assignments for a scratch-off discount is NOT legitimate?

Accepted Answer

Option d) because it includes a negative probability.

Question 5

Given $$A = \{1, 2, 3, 4, 5, 6, 7, 8\}$$ and $$B = \{3, 6, 9, 12\}$$, what is $$A \cap B$$?

Accepted Answer

$$\{3, 6\}$$

Question 6

What is the probability of tossing a coin and getting 'heads' 5 times in a row?

Accepted Answer

$$\left(\frac{1}{2}\$$right)^5$$ = \frac{1}{32}$$

Question 7

A 6-question multiple choice test has four answer choices per question. If you guess on all questions, what is the probability you get all 6 correct?

Accepted Answer

$$\left(\frac{1}{4}\$$right)^6$$ = \frac{1}{4096}$$

Question 8

What is the probability of rolling a die and NOT getting a '1' at all in three rolls?

Accepted Answer

$$\left(\frac{5}{6}\$$right)^3$$ = \frac{125}{216}$$

Question 9

If $$P(A) = 0.3$$, what is the probability that event $$A$$ does NOT occur?

Accepted Answer

$$1 - 0.3 = 0.7$$

Question 10

A consumer organization estimates that over a 1-year period, 17% of cars need one repair, 7% need two repairs, and 4% need three or more repairs. What is the probability that a randomly chosen car needs no repairs?

Accepted Answer

$$1 - (0.17 + 0.07 + 0.04) = 0.72$$

Question 11

Suppose 37% of voters are Democrats, 29% are Republicans, and 11% are members of other parties. What is the probability that a randomly selected voter is Independent?

Accepted Answer

$$1 - (0.37 + 0.29 + 0.11) = 0.23$$

Question 12

A slot machine has three wheels, each with 10 symbols: 4 bars, 3 lemons, 2 cherries, and 1 bell. What is the probability of getting 3 lemons?

Accepted Answer

$$\left(\frac{3}{10}\$$right)^3$$ = \frac{27}{1000}$$

Question 13

If you flip a coin until you get a tail or 3 consecutive heads, which of the following is NOT a possible outcome?

Accepted Answer

THH

Question 14

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

Accepted Answer

$$0.4 + 0.3 = 0.7$$

Question 15

What is the probability of getting at least one question correct on a 6-question multiple choice test (4 choices each) if you guess on all questions?

Accepted Answer

$$1 - \left(\frac{3}{4}\$$right)^6$$ \approx 0.822$$

Question 16

If you select four cars at random, and the probability that a car needs no repairs is $$0.72$$, what is the probability that none of the four cars need repairs?

Accepted Answer

$$0.72^4$$ \approx 0.268$$

Question 17

A slot machine has three wheels, each with 10 symbols: 4 bars, 3 lemons, 2 cherries, and 1 bell. What is the probability of getting no fruit symbols (bars or bell only) on all three wheels?

Accepted Answer

$$\left(\frac{4+1}{10}\$$right)^3$$ = \left(\frac{5}{10}\$$right)^3$$ = \frac{1}{8}$$

Probability Concepts and Rules: Study Guide for Introductory Statistics

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