5. Statistics and Probability

Conditional Probability — Quiz

Test your understanding of conditional probability with 5 practice questions.

Practice Questions

Question 1

A fair coin is tossed. If it lands on heads, a fair six-sided die is rolled. If it lands on tails, a fair four-sided die is rolled. What is the probability of rolling a $3$?

Question 2

In a city, $30\%$ of the population has a certain disease. A test for the disease has a $90\%$ true positive rate (correctly identifies those with the disease) and an $80\%$ true negative rate (correctly identifies those without the disease). If a randomly selected person tests positive, what is the probability that they actually have the disease?

Question 3

A bag contains $5$ red balls and $3$ blue balls. Two balls are drawn in succession without replacement. What is the probability that the first ball is red and the second ball is blue?

Question 4

A company has two machines, A and B, that produce widgets. Machine A produces $60\%$ of the widgets and Machine B produces $40\%$ of the widgets. $5\%$ of the widgets from Machine A are defective, and $10\%$ of the widgets from Machine B are defective. If a randomly selected widget is found to be defective, what is the probability that it was produced by Machine A?

Question 5

A student is taking two courses, Math and English. The probability of passing Math is $0.7$, and the probability of passing English is $0.8$. The probability of passing both courses is $0.6$. What is the probability that the student passes English given that they passed Math?