Q: Given the probability tree for fixing a device, what is the probability that a minor adjustment will fix the problem?

$$0.60 \times 0.80 + 0.30 \times 0.50 + 0.10 \times 0.10 = 0.64$$

Q: Which rule should you use to find the probability that either of two events occurs, even if they are not disjoint?

General Addition Rule: $$P(A \text{ or } B) = P(A) + P(B) - P(A \text{ and } B)$$

Question 1

Which of the following best describes the Law of Large Numbers?

Accepted Answer

It states that as the number of independent trials increases, the long-run relative frequency of an event approaches a single value.

Question 2

A store survey found that 56% of homes had at least 2 bathrooms, 62% were low priced, and 22% were both. What is the probability that a randomly selected home is high priced and has at least 2 bathrooms?

Accepted Answer

$$0.56 - 0.22 = 0.34$$

Question 3

Which of the following is NOT a valid method for estimating probability?

Accepted Answer

Law of Averages probability

Question 4

If $$P(A) = 0.3$$ and $$P(B) = 0.5$$, and A and B are independent, what is $$P(A 	ext{ and } B)$$?

Accepted Answer

$$0.3 	imes 0.5 = 0.15$$

Question 5

Which statement about disjoint (mutually exclusive) events is correct?

Accepted Answer

Disjoint events have no outcomes in common.

Question 6

Given the probability tree for fixing a device, what is the probability that a minor adjustment will fix the problem?

Accepted Answer

$$0.60 	imes 0.80 + 0.30 	imes 0.50 + 0.10 	imes 0.10 = 0.64$$

Question 7

If $$P(A) = 0.4$$, what is the probability of the complement of A?

Accepted Answer

$$1 - 0.4 = 0.6$$

Question 8

A contingency table shows that 91 out of 478 women prefer a camera. What is the conditional probability that a randomly selected woman prefers a camera?

Accepted Answer

$$91 / 251 = 0.362$$

Question 9

Which formula represents Bayes’s Rule for updating probability estimates?

Accepted Answer

$$P(A|B) = \frac{P(B|A)P(A)}{\sum_{i} P(B|A_i)P(A_i)}$$

Question 10

Which of the following is a common bias in subjective probability assessment?

Accepted Answer

Overconfidence bias

Question 11

If $$P(A) = 0.7$$ and $$P(B|A) = 0.2$$, what is $$P(A 	ext{ and } B)$$ using the General Multiplication Rule?

Accepted Answer

$$0.7 	imes 0.2 = 0.14$$

Question 12

Which of the following is true about the probability of the sample space?

Accepted Answer

It is always equal to 1.

Question 13

If two events are independent, which of the following must be true?

Accepted Answer

$$P(B|A) = P(B)$$

Question 14

A probability tree shows that the probability of fixing a device with a memory adjustment is 0.30, and the probability that this adjustment fixes the device is 0.50. What is the joint probability that a memory adjustment fixes the device?

Accepted Answer

$$0.30 	imes 0.50 = 0.15$$

Question 15

Which of the following is a marginal probability?

Accepted Answer

The probability that a randomly selected customer is a woman.

Question 16

Which rule should you use to find the probability that either of two events occurs, even if they are not disjoint?

Accepted Answer

General Addition Rule: $$P(A 	ext{ or } B) = P(A) + P(B) - P(A 	ext{ and } B)$$

Question 17

Which of the following is NOT a recommended practice when working with probabilities?

Accepted Answer

Adding probabilities of events that are not disjoint.

Chapter 8: Randomness and Probability – Study Notes for Introductory Statistics

Guida di studio - Domande di pratica

Study guide - Flashcard