2. Mathematical Foundations

Probability Theory — Quiz

Test your understanding of probability theory with 5 practice questions.

Practice Questions

Question 1

Which of the following distributions is most appropriate for modeling the number of successes in a fixed number of independent Bernoulli trials?

Question 2

Given a continuous random variable $X$ with a probability density function (PDF) $f(x)$, what is the probability that $X$ falls within the interval $[a, b]$?

Question 3

In the context of probability theory, what does the term 'sample space' refer to?

Question 4

If events A and B are mutually exclusive, what is the probability of their intersection, $P(A \cap B)$?

Question 5

Consider a scenario where an AI system is used for spam detection. Let $S$ be the event that an email is spam, and $F$ be the event that the AI system flags an email as spam. If $P(S) = 0.1$ (10% of emails are spam), $P(F|S) = 0.98$ (98% of spam emails are correctly flagged), and $P(F|\neg S) = 0.05$ (5% of non-spam emails are incorrectly flagged as spam), what is the probability that an email is actually spam given that the AI system flagged it as spam, i.e., $P(S|F)$?