Q: Which of the following statements is TRUE about independent events?

If two events are independent, $$P(E \text{ and } F) = P(E) \cdot P(F).$$

Q: Which probability rule should you use to find the probability that at least one of several independent events occurs?

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

Question 1

A simulation of rolling a 10-sided die 40 times resulted in a '4' being rolled 6 times. What is the empirical probability of rolling a '4' based on this simulation?

Accepted Answer

$$0.15$$

Question 2

According to the Law of Large Numbers, what happens to the relative frequency of an event as the number of trials increases?

Accepted Answer

It approaches the theoretical probability.

Question 3

In a simulation where 10,000 families each have four children, the probability that the fifth child is a boy, given the first four are girls, is closest to:

Accepted Answer

$$0.50$$

Question 4

Which of the following best describes the Law of Averages as discussed in probability theory?

Accepted Answer

It is a misconception that past outcomes affect future probabilities in independent trials.

Question 5

Given the Venn diagram where $$E = \{1,3,5,7,9\}$$ and $$F = \{0,1,2,3,4\}$$, what is $$P(E 	ext{ or } F) if $$the sample space $$S = \{0,1,2,3,4,5,6,7,8,9\}$$?

Accepted Answer

$$0.8$$

Question 6

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

$$0.83$$

Question 7

Which of the following is the correct formula for the complement rule?

Accepted Answer

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

Question 8

According to the travel time table, what is the probability that a randomly selected resident has a travel time of 90 or more minutes if the total number of residents is 400,000?

Accepted Answer

$$\frac{4,895}{400,000}$$

Question 9

Which of the following statements is TRUE about independent events?

Accepted Answer

If two events are independent, $$P(E 	ext{ and } F) = P(E) \cdot P(F).$$

Question 10

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

$$12$$

Question 11

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

Accepted Answer

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

Question 12

If you randomly select 4 out of 10 horses to receive a treat, and order does NOT matter, how many ways can this be done?

Accepted Answer

$$\frac{10!}{4!6!}$$

Question 13

Which probability rule should you use to find the probability that at least one of several independent events occurs?

Accepted Answer

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

Question 14

A probability model must satisfy which two conditions?

Accepted Answer

All probabilities are between 0 and 1, and their sum is 1.

Question 15

If $$P(E|F) = 0.4$$ and $$P(F) = 0.5$$, what is $$P(E 	ext{ and } F)$$?

Accepted Answer

$$0.2$$

Question 16

Which of the following is an example of a subjective probability?

Accepted Answer

A meteorologist predicts a 30% chance of rain based on experience.

Question 17

If you are making a sequence of choices and the order matters, which counting technique should you use?

Accepted Answer

Permutations

Chapter 5 STATS

Guida di studio - Domande di pratica

Study guide - Flashcard