DS 102 - QUIZ

What does 𝑃(𝐴∣𝐵)P(A∣B) represent in Bayes' Theorem?

• a) Prior probability
  

• b) Likelihood
  

• c) Posterior probability
  

• d) Marginal probability

In Bayes' Theorem, which component is used as a normalization factor?

• a) 𝑃(𝐴∣𝐵)

• b) 𝑃(𝐵∣𝐴)

• c) 𝑃(𝐴)

• d) 𝑃(𝐵)

Which term represents the initial belief about the likelihood of event A happening?

• a) Posterior probability
  

• b) Likelihood
  

• c) Prior probability
  

• d) Marginal probability

A factory produces 70% of its lightbulbs from Machine A, which has a defect rate of 2%. What is the likelihood of getting a defective bulb from Machine A?

• a) 70%
  

• b) 2%
  

• c) 68%
  

• d) 5%

If the prior probability of having a disease is 0.01 and the test's accuracy is 90%, which component does 0.01 represent in Bayes' Theorem?

• a) 𝑃(𝐴∣𝐵)
  

• b) 𝑃(𝐵∣𝐴)
  

• c) 𝑃(𝐴)

• d) 𝑃(𝐵)

A weather forecast is correct 70% of the time when it predicts rain. What is this probability in Bayes' Theorem terms?

• a) Prior probability
  

• b) Likelihood
  

• c) Posterior probability
  

• d) Marginal probability

In a medical diagnosis scenario, a positive test result occurs for healthy individuals 5% of the time. What does this 5% represent in Bayes' Theorem terms?

• a) 𝑃(𝐴∣𝐵)

• b) 𝑃(𝐵∣𝐴)

• c) 𝑃(𝐵∣¬𝐴)

• d) 𝑃(𝐴)

What does the Fundamental Counting Principle state?

• a) If one event can happen in m ways and another independent event can happen in n ways, then the combined number of ways for both events to occur is 𝑚+𝑛.

• b) If one event can happen in m ways and another independent event can happen in n ways, then the combined number of ways for both events to occur is 𝑚×𝑛.

• c) If one event can happen in m ways and another independent event can happen in n ways, then the combined number of ways for both events to occur is 𝑚−𝑛.

• d) If one event can happen in m ways and another independent event can happen in n ways, then the combined number of ways for both events to occur is 𝑚/𝑛.

How many ways can 4 books be arranged on a shelf?

• a) 12

• b) 16

• c) 24

• d) 32

What is the number of combinations for choosing 3 objects from a set of 5 distinct objects?

• a) 5
  

• b) 10
  

• c) 15
  

• d) 20