Question 1

Which of the following best describes the sample space for tossing two coins?

Accepted Answer

The set of all possible outcomes: $$\{HH, HT, TH, TT\}$$

Question 2

If $$A is $$the event of getting at most one tail when tossing two coins, what is $$P(A)$$?

Accepted Answer

$$\frac{3}{4}$$

Question 3

Given the sample space $$S = \{1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19\}$$, what is the probability of selecting an even number?

Accepted Answer

$$\frac{9}{19}$$

Question 4

If $$A$$ and $$B$$ are mutually exclusive events, which of the following is true?

Accepted Answer

$$P(A \cap B) = 0$$

Question 5

A new hire has a $$0.10$$ probability of staying 4 years and a $$0.05$$ probability of staying 5 years. What is the probability the new hire stays at least 4 years?

Accepted Answer

$$0.15$$

Question 6

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

Accepted Answer

$$0.2$$

Question 7

Which of the following is the correct formula for the complement of event $$A$$?

Accepted Answer

$$P(A^c) = 1 - P(A)$$

Question 8

Suppose the probability distribution for $$X is $$given by $$P(X=0)=0.02$$, $$P(X=1)=0.08$$, $$P(X=2)=0.90. $$What is the expected value $$E[X]$$?

Accepted Answer

$$1.88$$

Question 9

If $$P(A) = 0.6$$, $$P(B) = 0.5$$, and $$P(A \cap B) = 0.3$$, what is $$P(A \cup B)$$?

Accepted Answer

$$0.8$$

Question 10

A student is randomly selected from a class. The probability the student is a sophomore is $$0.85$$, and the probability the student is an athlete is $$0.20. If $$being a sophomore and being an athlete are independent, what is the probability the student is both a sophomore and an athlete?

Accepted Answer

$$0.17$$

Question 11

Which of the following best defines 'equally likely outcomes'?

Accepted Answer

Outcomes that have the same probability of occurring

Question 12

If $$P(A) = 0.7$$ and $$P(B) = 0.2$$, and $$A$$ and $$B$$ are mutually exclusive, what is $$P(A \cup B)$$?

Accepted Answer

$$0.9$$

Question 13

A fair die is rolled. What is the probability of getting a number greater than 4?

Accepted Answer

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

Question 14

If $$P(A) = 0.4$$, $$P(B) = 0.3$$, and $$P(A \cap B) = 0.1$$, what is $$P(A \cup B)$$?

Accepted Answer

$$0.6$$

Question 15

Which of the following is NOT a valid probability value?

Accepted Answer

$$1.2$$

Question 16

If the probability of being born on February 29 is $$0.00274$$, what is the probability of NOT being born on February 29?

Accepted Answer

$$0.99726$$

Question 17

Suppose $$P(A) = 0.3$$, $$P(B) = 0.4$$, and $$A$$ and $$B$$ are independent. What is $$P(A \cap B)$$?

Accepted Answer

$$0.12$$

Question 18

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

Accepted Answer

$$0.75$$

Question 19

A probability distribution for $$X is $$given as $$P(X=1)=0.12$$, $$P(X=2)=0.30$$, $$P(X=3)=0.15$$, $$P(X=4)=0.10$$, $$P(X=5)=0.05. $$What is the probability that $$X \geq 4$$?

Accepted Answer

$$0.15$$

Question 20

If $$P(A) = 0.6$$, $$P(B) = 0.5$$, and $$P(A \cap B) = 0.3$$, what is $$P(A^c \cap B)$$?

Accepted Answer

$$0.2$$

Fundamentals of Probability and Probability Distributions

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