1. Foundations

Probability Basics — Quiz

Test your understanding of probability basics with 5 practice questions.

Practice Questions

Question 1

Given events $B$ and $B^c$ partition the sample space with $P(B)=0.4$, $P(A\mid B)=0.7$, and $P(A\mid B^c)=0.2$, what is $P(A)$ according to the law of total probability?

Question 2

In a medical test scenario, let $D$ be disease presence with $P(D)=0.01$, and the test has $P(+\mid D)=0.95$ and $P(+\mid D^c)=0.02$. What is the posterior probability $P(D\mid +)$?

Question 3

Let $X$ be a discrete random variable with $P(X=1)=0.2$, $P(X=2)=0.3$, and $P(X=3)=0.5$. What is $E[X^2]$?

Question 4

Given a discrete random variable $X$ with $P(0)=0.1$, $P(1)=0.2$, $P(2)=0.3$, and $P(3)=0.4$, compute the conditional expectation $E[X\mid X\ge2]$.

Question 5

Which equation correctly characterizes the conditional independence of events $A$ and $B$ given $C$?