2. Probability Theory

Probability Basics — Quiz

Test your understanding of probability basics with 5 practice questions.

Practice Questions

Question 1

A continuous random variable $X$ has a probability density function (PDF) given by $f(x) = cx$ for $0 \le x \le 4$, and $f(x) = 0$ otherwise. What is the value of the constant $c$?

Question 2

Consider two events $A$ and $B$ such that $P(A) = 0.6$, $P(B) = 0.7$, and $P(B|A) = 0.5$. What is the probability of event A occurring given event B has occurred, $P(A|B)$?

Question 3

A fair coin is tossed $5$ times. What is the probability of getting exactly $3$ heads?

Question 4

In a group of $200$ students, $120$ are enrolled in Calculus, $80$ are enrolled in Physics, and $40$ are enrolled in both. What is the probability that a randomly selected student is enrolled in neither Calculus nor Physics?

Question 5

A bag contains $6$ red balls and $4$ blue balls. If two balls are drawn one after the other without replacement, what is the probability that the first ball is red and the second ball is also red?