Question 1

A factory produces widgets with a defect rate of 10%. If a customer buys 5 widgets, what is the probability that at least one widget is defective? Use the complement rule.

Accepted Answer

$$1 - (0.9)^5$

Question 2

Which of the following best describes the meaning of 'at least one' in probability problems?

Accepted Answer

One or more occurrences of the event

Question 3

Suppose the probability that a student cracks their phone screen at a concert is 0.08. If 8 students attend, what is the probability that none of them cracks their screen?

Accepted Answer

$$(1 - 0.08)^8$

Question 4

In a group project, 15% of students do not contribute. If you are assigned to a group of 4, what is the probability that all students contribute?

Accepted Answer

$$(0.85)^4$$

Question 5

If the probability of a match ghosting you on a dating app is 0.25, and you match with 5 people, what is the probability that at least one person replies?

Accepted Answer

$$1 - (0.75)^5$

Question 6

Which formula correctly expresses the conditional probability of event B given event A?

Accepted Answer

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

Question 7

A pre-employment drug test yields a positive result for 45 out of 50 drug users. What is the probability that a drug user tests positive?

Accepted Answer

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

Question 8

Given that a subject had a positive drug test result, and 45 out of 70 positive results were from drug users, what is the probability that a subject with a positive result actually uses drugs?

Accepted Answer

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

Question 9

Which statement is true regarding conditional probabilities?

Accepted Answer

$$P(B|A) is $$generally not equal to $$P(A|B)$$

Question 10

If $$P(D|M) = 1$$ and $$P(M|D) = 0$$, what does this illustrate?

Accepted Answer

Confusion of the inverse

Question 11

A company wants to reduce the probability of at least one defective product in a batch of 12 to below 0.5. What is the maximum defect rate $$p$$ that will achieve this goal?

Accepted Answer

$$(1-p)^{12}$$ \u003e 0.5$$

Question 12

Which of the following is the complement of the event 'at least one defective product' in a sample of $$n$$ products?

Accepted Answer

No products are defective

Question 13

If $$P(A) = 0.3$$ and $$P(B) = 0.5$$, and $$A$$ and $$B$$ are independent, what is $$P(A \cap B)$$?

Accepted Answer

$$0.15$$

Question 14

Which scenario best illustrates the use of the multiplication rule in probability?

Accepted Answer

Finding the probability that two independent events both occur

Question 15

A student is confused and thinks $$P(B|A) = P(A|B). $$What is this error called?

Accepted Answer

Confusion of the inverse

Question 16

If the probability of a student not contributing to a group project is 0.15, what is the probability that in a group of 4, at least one does not contribute?

Accepted Answer

$$1 - (0.85)^4$

Question 17

Which of the following is NOT a correct application of the complement rule?

Accepted Answer

Calculating the probability of exactly one event by subtracting the probability of more than one from 1

Probability: Complements, Conditional Probability, and the Multiplication Rule

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