Q: Which of the following is a correct application of the General Multiplication Rule?

$P(A \text{ and } B) = P(A) \times P(B|A)$

Question 1

Which of the following best describes the Law of Large Numbers (LLN)?

Accepted Answer

As the number of trials increases, the long-run relative frequency of an event gets closer to a single value.

Question 2

A manager wants to estimate the probability that a new product will be successful based on their own experience and intuition, rather than data or models. What type of probability is this?

Accepted Answer

Subjective probability

Question 3

If two events are disjoint (mutually exclusive), which of the following statements is true?

Accepted Answer

They cannot be independent.

Question 4

A company finds that 56% of homes have at least two bathrooms, 62% are low-priced, and 22% are both low-priced and have at least two bathrooms. What is the probability that a randomly selected home is either low-priced or has at least two bathrooms?

Accepted Answer

$0.62 + 0.56 - 0.22 = 0.96$

Question 5

Which formula correctly represents the probability of the complement of event $A$?

Accepted Answer

$P(A^C) = 1 - P(A)$

Question 6

A contingency table shows that 91 out of 478 customers are women who prefer a camera. What is the joint probability that a randomly selected customer is a woman and prefers a camera?

Accepted Answer

$\frac{91}{478} = 0.190$

Question 7

Which of the following is NOT a cognitive bias that can affect the interpretation of statistical information?

Accepted Answer

Law of Large Numbers bias

Question 8

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

Accepted Answer

$0.4 	imes 0.5 = 0.2$

Question 9

A misleading graph shows the cost of gas rising steeply, but the vertical axis is truncated. What is the main issue with this presentation?

Accepted Answer

It exaggerates the perceived increase by manipulating the axis scale.

Question 10

Which of the following is the correct formula for Bayes’s Rule for two events $A$ and $B$?

Accepted Answer

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

Question 11

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

Accepted Answer

$0.60 	imes 0.80 = 0.48$

Question 12

Which of the following statements about probability is FALSE?

Accepted Answer

The probability of all possible outcomes in a sample space must add up to more than 1.

Question 13

A manager claims that because a coin landed on heads five times in a row, it is 'due' to land on tails next. This is an example of:

Accepted Answer

The nonexistent Law of Averages

Question 14

If $P(A) = 0.7$, $P(B) = 0.5$, and $P(A 	ext{ and } B) = 0.3$, what is $P(A 	ext{ or } B)$?

Accepted Answer

$0.7 + 0.5 - 0.3 = 0.9$

Question 15

Which of the following is an example of the base rate fallacy?

Accepted Answer

Believing that winning the lottery is common because someone you know won.

Question 16

A contingency table shows that 30 out of 251 women prefer a bike. What is the probability that a randomly selected woman prefers a bike?

Accepted Answer

$\frac{30}{251} = 0.120$

Question 17

Which of the following is a correct application of the General Multiplication Rule?

Accepted Answer

$P(A 	ext{ and } B) = P(A) 	imes P(B|A)$

Question 18

A misleading infographic shows McDonald's sales as a bar four times as high and four times as wide as Burger King's, even though McDonald's sales are only 3.6 times higher. What is the main issue with this graph?

Accepted Answer

It exaggerates the difference by using area instead of height to represent values.

Question 19

Which of the following is a marginal probability?

Accepted Answer

The probability that a randomly selected customer is a woman.

Chapter 8: Randomness and Probability - Business Statistics Study Notes

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