Q: Which of the following is the correct formula for the probability of the union of two events A and B?

$$P(A \text{ or } B) = P(A) + P(B) - P(A \text{ and } B)$$

Q: If two events A and B are independent, which of the following is true?

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

Q: If two subjects are selected with replacement from a group where 50 use drugs (45 test positive, 5 test negative), what is the probability that the first selected person tests positive and the second tests negative?

$$\frac{45}{50} \times \frac{5}{50}$$

Q: Which of the following is a correct application of the addition rule for two non-disjoint events A and B?

$$P(A \text{ or } B) = P(A) + P(B) - P(A \text{ and } B)$$

Question 1

Which of the following best describes a compound event in probability?

Accepted Answer

An event that combines two or more simple events.

Question 2

If events A and B are disjoint, which of the following is true?

Accepted Answer

$$P(A 	ext{ and } B) = 0$$

Question 3

Given the following table for a drug test:

- 45 subjects use drugs and test positive
- 5 subjects use drugs and test negative
- 25 subjects do not use drugs and test positive
- 480 subjects do not use drugs and test negative

What is the probability that a randomly selected subject actually uses drugs, given that they had a positive test result?

Accepted Answer

$$\frac{45}{70}$$

Question 4

Which of the following is the correct formula for the probability of the union of two events A and B?

Accepted Answer

$$P(A 	ext{ or } B) = P(A) + P(B) - P(A 	ext{ and } B)$$

Question 5

A factory produces products with a defect rate of 15%. If a customer purchases 12 products, what is the probability that at least one is defective?

Accepted Answer

$$1 - (0.85$$)^{12}$$

Question 6

If two events A and B are independent, which of the following is true?

Accepted Answer

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

Question 7

A Seagate hard drive has a failure rate of 2.89% in a year. If your computer has two such drives, what is the probability that at least one will work for a year?

Accepted Answer

$$1 - (0.9711)^2$

Question 8

If two subjects are selected with replacement from a group where 50 use drugs (45 test positive, 5 test negative), what is the probability that the first selected person tests positive and the second tests negative?

Accepted Answer

$$\frac{45}{50} 	imes \frac{5}{50}$$

Question 9

Which of the following best describes conditional probability?

Accepted Answer

The probability of an event occurring given that another event has occurred.

Question 10

Given the drug test table, what is the probability that a randomly selected subject who uses drugs tests positive?

Accepted Answer

$$\frac{45}{50}$$

Question 11

If two events are not independent, what does this imply?

Accepted Answer

The occurrence of one event affects the probability of the other.

Question 12

If you sample without replacement and the sample size is no more than 5% of the population, how should you treat the selections?

Accepted Answer

Treat the selections as independent.

Question 13

Which of the following is a correct application of the addition rule for two non-disjoint events A and B?

Accepted Answer

$$P(A 	ext{ or } B) = P(A) + P(B) - P(A 	ext{ and } B)$$

Question 14

A subject is randomly selected from the drug test table. What is the probability that the subject does not use drugs and tests negative?

Accepted Answer

$$\frac{480}{555}$$

Question 15

Which of the following is an example of a real-world application of the 'at least one' probability rule?

Accepted Answer

Calculating the probability that at least one product in a batch of 12 is defective.

Compound Events and Probability Rules in Statistics

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