Q: If $$P(A) = 0.3$$, $$P(B) = 0.4$$, and $$P(A \text{ and } B) = 0.12$$, are A and B independent?

Yes, because $$P(A \text{ and } B) = P(A) \times P(B)$$

Question 1

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

Accepted Answer

It states that as the number of trials increases, the long-run relative frequency of an event gets closer to 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

$$0.34$$

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

$$0.15$$

Question 5

Which of the following statements 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

$$0.64$$

Question 7

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

Accepted Answer

$$0.6$$

Question 8

A contingency table shows that $$P(woman) = 0.525$$ and $$P(woman 	ext{ and } camera) = 0.190. $$What is $$P(camera|woman)$$?

Accepted Answer

$$0.362$$

Question 9

Which of the following is a source of bias in subjective probability?

Accepted Answer

Overconfidence bias

Question 10

If two events A and B are disjoint, which rule should be used to find $$P(A 	ext{ or } B)$$?

Accepted Answer

Addition Rule

Question 11

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 12

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

$$0.14$$

Question 13

Which of the following is a marginal probability?

Accepted Answer

$$P(woman)$$

Question 14

If $$P(A) = 0.3$$, $$P(B) = 0.4$$, and $$P(A 	ext{ and } B) = 0.12$$, are A and B independent?

Accepted Answer

Yes, because $$P(A 	ext{ and } B) = P(A) 	imes P(B)$$

Question 15

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

Accepted Answer

Adding probabilities of events that are not disjoint

Question 16

A probability tree shows that the probability of a case adjustment is $$0.60$$ and the probability it fixes the problem is $$0.80. $$What is the probability that a case adjustment fixes the problem?

Accepted Answer

$$0.48$$

Question 17

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

Accepted Answer

General Addition Rule

Question 18

If $$P(A) = 0.5$$, $$P(B) = 0.4$$, and $$P(A 	ext{ or } B) = 0.7$$, what is $$P(A 	ext{ and } B)$$?

Accepted Answer

$$0.2$$

Question 19

Which of the following best describes a subjective probability?

Accepted Answer

It expresses personal uncertainty and may be influenced by bias.

Question 20

In a contingency table, what type of probability is $$P(bike|woman)$$?

Accepted Answer

Conditional probability

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

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