Practice Conditional Probability in Math

Use these practice problems to test your method after reviewing the concept explanation and worked examples.

Quick Recap

The conditional probability P(A|B) is the probability of event A occurring given that event B has already occurred.

If I know B happened, what's the chance of A? Updates probability with new info.

Example 1

medium
In a class of 30 students, 18 play soccer, 12 play basketball, and 6 play both. If a student plays soccer, what is the probability they also play basketball?

Example 2

hard
A test for a disease is 95\% accurate (true positive rate) with a 3\% false positive rate. If 1\% of the population has the disease, what is the probability a person who tests positive actually has the disease?

Example 3

medium
Two cards are drawn without replacement from a standard deck. Given that the first card is a king, what is the probability the second card is also a king?

Example 4

hard
A jar contains 6 red marbles and 4 blue marbles. Two marbles are drawn without replacement. Given that at least one marble is blue, what is the probability both marbles are blue?
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