Question 1

Which of the following best describes a probability experiment?

Accepted Answer

A test that allows us to measure possible experiment results/outcomes, usually with more than one possible result.

Question 2

Given the sample space $$S = \{1, 2, 3, 4, 5, 6\}$$ for a fair die, what is the event $$A if$$ $$A is $$defined as 'the outcome is an even number'?

Accepted Answer

$$A = \{2, 4, 6\}$$

Question 3

If you roll a fair die and then toss a fair coin, how many possible outcomes are there?

Accepted Answer

12

Question 4

Which notation correctly represents the complement of set $$A in $$the universal set $$U$$?

Accepted Answer

$$A'$$

Question 5

Let $$A = \{2, 3, 5, 7, 11, 13\}. $$What is the cardinality of $$A$$?

Accepted Answer

$$|A| = 6$$

Question 6

What is the cardinality of the power set $$P(A) if$$ $$A = \{1, 2, 3, 4\}$$?

Accepted Answer

$$|P(A)| = 16$$

Question 7

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

Accepted Answer

Disjoint events have no elements in common, i.e., $$A \cap B = \varphi.$$

Question 8

Let $$U = \{1, 2, 3, 4, 5, 6, 7, 8, 9, 10\}$$, $$A = \{1, 3, 5, 7, 9\}$$, and $$B = \{2, 3, 5, 7\}. $$What is $$A \cap B$$?

Accepted Answer

$$\{3, 5, 7\}$$

Question 9

If the outcomes of a sample space are equally likely and there are $$n$$ outcomes, what is the probability of any single outcome?

Accepted Answer

$$\frac{1}{n}$$

Question 10

A statistics class consists of 25 industrial, 10 mechanical, 10 electrical, and 8 civil engineering students. If a student is randomly selected, what is the probability that the student is an industrial engineering major?

Accepted Answer

$$\frac{25}{53}$$

Question 11

A die is loaded so that an even number is twice as likely to occur as an odd number. What is the probability that a number less than 4 occurs on a single toss?

Accepted Answer

$$\frac{3}{8}$$

Question 12

If $$P(A) = 0.8$$, $$P(B) = 0.6$$, and $$P(A \cap B) = 0.5$$, what is the probability that at least one of $$A or$$ $$B$$ occurs?

Accepted Answer

$$0.9$$

Question 13

Which formula correctly represents the probability of the union of three events $$A$$, $$B$$, and $$C$$?

Accepted Answer

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

Question 14

Suppose you toss three fair coins at the same time. What is the probability that the sum of the results is exactly one?

Accepted Answer

$$\frac{3}{8}$$

Question 15

Which of the following is NOT a valid axiom of probability theory?

Accepted Answer

$$P(E) \u003e 1$$ for some event $$E$$

Question 16

Which of the following is a correct statement of De Morgan’s law?

Accepted Answer

$$(A \cap B)^c = A^c \cup B^c$$

Question 17

If the probability that a randomly produced cable meets specifications is $$0.99$$, and the probability that a cable is too large is equal to the probability that it is too small, what is the probability that a cable is too large?

Accepted Answer

$$0.005$$

Question 18

If a pair of fair dice is tossed, what is the probability of getting a total of 7 or 11?

Accepted Answer

$$\frac{8}{36}$$

Probability Models and Set Theory in Statistics

스터디 가이드 - 연습 문제

학습 가이드 - 플래시카드