Q: Which of the following is a correct application of the General Addition Rule for two events $$E$$ and $$F$$?

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

Q: Which formula should you use to find the probability that at least one of $$n$$ independent events occurs?

$$P(\text{at least one}) = 1 - P(\text{none})$$

Q: If you want to find the probability that a randomly selected household has high-speed internet, given that it has land-line phone service, which formula should you use?

$$P(\text{Internet} | \text{Land-line}) = \frac{P(\text{Internet and Land-line})}{P(\text{Land-line})}$$

Question 1

A simulation of rolling a 10-sided die 40 times resulted in a proportion of 0.15 for rolling a '4'. According to the Law of Large Numbers, what would you expect to happen to this proportion as the number of rolls increases to 1000?

Accepted Answer

The proportion will get closer to the true probability of rolling a '4', which is $$\frac{1}{10}.$$

Question 2

In a probability experiment, the sample space $$S$$ consists of all possible outcomes. If $$E is an $$event, which of the following best describes the complement $$E^c$$?

Accepted Answer

$$E^c is $$the set of all outcomes in $$S$$ that are not in $$E.$$

Question 3

Suppose you simulate 10,000 families, each with four children, where the probability of having a girl is 0.5 for each child. Among families with four girls, what is the probability that the fifth child is a boy?

Accepted Answer

0.5

Question 4

Which of the following is a correct application of the General Addition Rule for two events $$E$$ and $$F$$?

Accepted Answer

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

Question 5

A travel survey reports the following frequencies for commute times: 4,895 people commute 90 or more minutes out of a total of 400,000 surveyed. What is the probability that a randomly selected person commutes less than 90 minutes?

Accepted Answer

$$P = 1 - \frac{4,895}{400,000}$$

Question 6

Which of the following statements about disjoint (mutually exclusive) and independent events is TRUE?

Accepted Answer

Independent events can have outcomes in common.

Question 7

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

$$0.32 + 0.61 - 0.10 = 0.83$$

Question 8

A restaurant offers 2 appetizers, 4 entrées, and 2 desserts. Using the multiplication rule of counting, how many different meals can be ordered?

Accepted Answer

$$2 	imes 4 	imes 2 = 16$$

Question 9

How many ways can the letters in the word 'MISSISSIPPI' be arranged?

Accepted Answer

$$\frac{11!}{4!4!2!1!}$$

Question 10

A probability model for the number of rooms in a housing unit lists probabilities for each possible number of rooms. What must the sum of all these probabilities equal?

Accepted Answer

$$1$$

Question 11

If the probability that a randomly selected 60-year-old female survives the year is 0.992, what is the probability that four randomly selected 60-year-old females all survive the year?

Accepted Answer

$$0.992^4$$

Question 12

Which formula should you use to find the probability that at least one of $$n$$ independent events occurs?

Accepted Answer

$$P(	ext{at least one}) = 1 - P(	ext{none})$$

Question 13

A pizza shop offers 8 toppings. How many different two-topping pizzas can be made if order does not matter and no topping is repeated?

Accepted Answer

$$\frac{8!}{2!6!} = 28$$

Question 14

Which of the following best describes a subjective probability?

Accepted Answer

A probability based on personal judgment or expert opinion.

Question 15

If you want to find the probability that a randomly selected household has high-speed internet, given that it has land-line phone service, which formula should you use?

Accepted Answer

$$P(	ext{Internet} | 	ext{Land-line}) = \frac{P(	ext{Internet and Land-line})}{P(	ext{Land-line})}$$

Chapter 5: Probability – Rules, Methods, and Applications

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