Q: Which of the following best describes the Addition Rule for disjoint (mutually exclusive) events E and F?

$$P(E \text{ or } F) = P(E) + P(F)$$

Q: Suppose you randomly select a chip labeled 0–9. Let $$E be $$the event 'choose an odd number' and $$F be $$the event 'choose a number less than or equal to 4.' What is $$P(E \text{ or } F)$$?

$$P(E \text{ or } F) = \frac{8}{10}$$

Q: A Venn diagram shows two overlapping circles E and F. What does the overlapping region represent?

The outcomes that are in both E and F ($$E \text{ and } F)$$

Question 1

Which of the following best describes the Addition Rule for disjoint (mutually exclusive) events E and F?

Accepted Answer

$$P(E 	ext{ or } F) = P(E) + P(F)$$

Question 2

Suppose you randomly select a chip labeled 0–9. Let $$E be $$the event 'choose an odd number' and $$F be $$the event 'choose a number less than or equal to 4.' What is $$P(E 	ext{ or } F)$$?

Accepted Answer

$$P(E 	ext{ or } F) = \frac{8}{10}$$

Question 3

If $$P(E) = 0.32$$, $$P(F) = 0.61$$, and $$P(E 	ext{ and } F) = 0.10$$, what is $$P(E 	ext{ or } F)$$?

Accepted Answer

$$P(E 	ext{ or } F) = 0.83$$

Question 4

If $$P(E) = 0.32$$ and $$P(F) = 0.61$$, and E and F are mutually exclusive, what is $$P(E 	ext{ or } F)$$?

Accepted Answer

$$P(E 	ext{ or } F) = 0.93$$

Question 5

Given the probability model for number of rooms in a housing unit, what is the probability that a randomly selected unit has two or three rooms?

Accepted Answer

$$0.032 + 0.093 = 0.125$$

Question 6

What is the probability that a randomly selected housing unit has one, two, or three rooms?

Accepted Answer

$$0.010 + 0.032 + 0.093 = 0.135$$

Question 7

A Venn diagram shows two overlapping circles E and F. What does the overlapping region represent?

Accepted Answer

The outcomes that are in both E and F ($$E 	ext{ and } F)$$

Question 8

According to the American Veterinary Medical Association, 31.6% of American households own a dog. What is the probability that a randomly selected household does NOT own a dog?

Accepted Answer

$$1 - 0.316 = 0.684$$

Question 9

Given the travel time data for Hartford County, CT, what is the probability that a randomly selected resident has a commute time of 90 or more minutes?

Accepted Answer

$$\frac{4895}{349281} \approx 0.014$$

Question 10

Using the complement rule, what is the probability that a randomly selected Hartford County resident has a commute time less than 90 minutes?

Accepted Answer

$$1 - \frac{4895}{349281} \approx 0.986$$

Question 11

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 12

Suppose in a population, 10% are widowed and 8% are divorced. What is the probability that a randomly selected person is widowed or divorced, assuming these events are disjoint?

Accepted Answer

$$0.10 + 0.08 = 0.18$$

Question 13

If $$P(A) = 0.4$$, $$P(B) = 0.5$$, and $$P(A 	ext{ and } B) = 0.2$$, what is $$P(A 	ext{ or } B)$$?

Accepted Answer

$$0.4 + 0.5 - 0.2 = 0.7$$

Question 14

Which of the following statements is TRUE about mutually exclusive events?

Accepted Answer

They cannot occur at the same time.

Question 15

A bag contains chips labeled 0–9. What is the probability of selecting a chip labeled with a number less than or equal to 2 or greater than or equal to 8?

Accepted Answer

$$\frac{3}{10} + \frac{2}{10} = \frac{5}{10}$$

Addition Rule and Complements in Probability

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