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, what is the probability that a randomly selected number has 1 as its first digit?

Accepted Answer

$$0.30$$

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

Question 6

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

Accepted Answer

$$\dfrac{4}{52} + \dfrac{13}{52} - \dfrac{1}{52}$$

Question 7

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

$$\dfrac{6}{36} + \dfrac{10}{36} - \dfrac{3}{36} = \dfrac{13}{36}$$

Question 8

Which of the following is the correct general addition rule for any two events $$A$$ and $$B$$?

Accepted Answer

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

Question 9

If $$P(E) = 0.52$$, what is the probability of the complement of $$E$$?

Accepted Answer

$$0.48$$

Question 10

Which of the following best describes the complement of an event $$E$$?

Accepted Answer

All outcomes in the sample space that are not in $$E$$

Question 11

Suppose the probability that a randomly selected American has played a state lottery is $$0.52. $$What is the probability that a randomly selected American has NOT played a state lottery?

Accepted Answer

$$0.48$$

Question 12

If $$A$$ and $$B$$ are mutually exclusive events, what is $$P(A \cap B)$$?

Accepted Answer

$$0$$

Question 13

A Venn diagram is useful in probability because:

Accepted Answer

It graphically represents events and their relationships within the sample space.

Question 14

If $$P(A) = 0.4$$, $$P(B) = 0.5$$, and $$P(A \cap B) = 0.2$$, what is $$P(A \cup B)$$?

Accepted Answer

$$0.7$$

Question 15

Which of the following is NOT a property of mutually exclusive events?

Accepted Answer

They can both occur at the same time.

Question 16

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 17

Which of the following real-world scenarios best illustrates the use of the complement rule?

Accepted Answer

Calculating the probability that a person has not been exposed to a certain disease, given the probability that they have been exposed.

Question 18

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

Accepted Answer

$$0.7$$

Question 19

Which of the following is the correct formula for the probability of the union of three pairwise disjoint events $$A$$, $$B$$, and $$C$$?

Accepted Answer

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

Question 20

A number is chosen at random from 1 to 9. According to Benford’s Law, what is the probability that the first digit is either 1 or 2?

Accepted Answer

$$0.30 + 0.18 = 0.48$$

Probability: Addition Rules and Complements

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