Q: A class has 25 students: 20 female and 5 male. If two students are chosen at random without replacement, what is the probability that both are male?

$$\frac{5}{25} \times \frac{4}{24}$$

Question 1

Which of the following best describes the sample space for the experiment of rolling a fair six-sided die until a 6 appears?

Accepted Answer

The set of all positive integers $$\{1,2,3,\ldots\}$$

Question 2

Suppose you flip a fair coin twice. What is the probability that at least one head appears?

Accepted Answer

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

Question 3

Which of the following is NOT an axiom of probability?

Accepted Answer

$$P(A \cup B) = P(A) + P(B)$$ for any events $$A$$ and $$B$$

Question 4

A manufacturer receives LED screens from three suppliers. Supplier 1 provides 65% of the screens, Supplier 2 provides 20%, and Supplier 3 provides 15%. If the probability that a screen from Supplier 2 is defective is 0.08, what is the probability that a randomly selected screen is both from Supplier 2 and defective?

Accepted Answer

$$0.016$$

Question 5

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

Accepted Answer

$$P(A \cup B) = P(A) + P(B)$$

Question 6

A class has 25 students: 20 female and 5 male. If two students are chosen at random without replacement, what is the probability that both are male?

Accepted Answer

$$\frac{5}{25} 	imes \frac{4}{24}$$

Question 7

Which formula correctly expresses the probability of the union of two events $$A$$ and $$B$$?

Accepted Answer

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

Question 8

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

Accepted Answer

$$0.3$$

Question 9

Which of the following statements about conditional probability is correct?

Accepted Answer

$$P(A|B) = \frac{P(A \cap B)}{P(B)}$$

Question 10

A coin is flipped three times. What is the probability of getting exactly two heads?

Accepted Answer

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

Question 11

Which of the following is the correct statement about the complement of an event $$A$$?

Accepted Answer

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

Question 12

Suppose $$P(A) = 0.4$$, $$P(B) = 0.5$$, and $$P(A \cap B) = 0.2. $$What is $$P(A \cup B)$$?

Accepted Answer

$$0.7$$

Question 13

If the probability of observing an even number when rolling a fair six-sided die is $$P(A)$$, what is $$P(A)$$?

Accepted Answer

$$\frac{1}{2}$$

Question 14

Which of the following is a correct application of Bayes’ rule?

Accepted Answer

$$P(B|A) = \frac{P(A|B)P(B)}{P(A)}$$

Question 15

A fair coin is flipped. What is the probability of getting a head or a tail?

Accepted Answer

$$1$$

Question 16

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

Accepted Answer

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

Question 17

A dentist’s office finds that 12% of elementary school patients fear visiting the dentist. If 40% of all patients are elementary school students, what is the probability that a randomly selected patient is both an elementary school student and fears visiting the dentist?

Accepted Answer

$$0.048$$

Question 18

Which method of assigning probability is most appropriate for estimating the chance of rain tomorrow?

Accepted Answer

Long-run relative frequency

Question 19

If $$P(A|B) 
eq P(A)$$, what does this imply about events $$A$$ and $$B$$?

Accepted Answer

They are dependent

Question 20

A coin is flipped twice. What is the probability that both flips are heads?

Accepted Answer

$$\frac{1}{4}$$

Probability: Foundations and Applications for Business Statistics

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