Question 1

Which of the following statements best describes disjoint (mutually exclusive) events?

Accepted Answer

They are events that have no outcomes in common.

Question 2

Suppose you randomly select a chip from a bag labeled 0 through 9. Let $$E be $$the event 'choose a number less than or equal to 2' and $$F be $$the event 'choose a number greater than or equal to 8'. What is $$P(E \cup F)$$?

Accepted Answer

$$0.5$$

Question 3

If $$E$$ and $$F$$ are disjoint events, which formula correctly gives the probability that either $$E or$$ $$F$$ occurs?

Accepted Answer

$$P(E \cup F) = P(E) + P(F)$$

Question 4

According to Benford’s Law, which digit is most likely to appear as the first digit in naturally occurring datasets?

Accepted Answer

1

Question 5

A card is drawn at random from a standard 52-card deck. Let $$A be $$the event 'the card is a diamond' and $$B be $$the event 'the card is a face card'. What is $$P(A \cup B)$$?

Accepted Answer

$$\dfrac{16}{52}$$

Question 6

Suppose a pair of dice are thrown. Let $$E be$$ 'the first die is a two' and $$F be$$ 'the sum of the dice is less than or equal to 5'. What is $$P(E \cup F)$$?

Accepted Answer

$$\dfrac{13}{36}$$

Question 7

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

Accepted Answer

$$P(E^C) = 1 - P(E)$$

Question 8

According to the National Gambling Impact Study Commission, 52% of Americans have played state lotteries. What is the probability that a randomly selected American has NOT played a state lottery?

Accepted Answer

$$0.48$$

Question 9

Which of the following best describes the union of two events $$A$$ and $$B$$?

Accepted Answer

The event that at least one of $$A or$$ $$B$$ occurs.

Question 10

If $$A$$ and $$B$$ are not disjoint, which formula should be used to find $$P(A \cup B)$$?

Accepted Answer

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

Question 11

A medical test for a rare disease has a 99% chance of correctly identifying a healthy person (true negative). If the probability that a randomly selected person has the disease is 0.01, what is the probability that a randomly selected person does NOT have the disease?

Accepted Answer

$$0.99$$

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

$$0.9$$

Question 13

Which of the following is a real-world example of mutually exclusive (disjoint) events?

Accepted Answer

Rolling a die and getting an even number or an odd number.

Question 14

If $$P(E) = 0.3$$ and $$P(F) = 0.2$$ and $$E$$ and $$F$$ are disjoint, what is $$P(E \cup F)$$?

Accepted Answer

$$0.5$$

Question 15

A company finds that the probability a randomly selected invoice starts with the digit 1 is 0.30, and with the digit 2 is 0.18 (according to Benford’s Law). What is the probability that a randomly selected invoice starts with either 1 or 2?

Accepted Answer

$$0.48$$

Question 16

Suppose $$P(A) = 0.6$$ and $$P(A^C) = x. $$What is the value of $$x$$?

Accepted Answer

$$0.4$$

Question 17

Which of the following is the correct interpretation of $$P(A \cap B)$$?

Accepted Answer

The probability that both $$A$$ and $$B$$ occur.

Probability: Addition Rules and Complements

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