Practice Independent Events in Math
Use these practice problems to test your method after reviewing the concept explanation and worked examples.
Quick Recap
Two events are independent if the occurrence of one does not change the probability of the other: P(A \cap B) = P(A) \cdot P(B).
They don't 'know about' each other. One happening tells you nothing about the other.
Example 1
easyA fair coin is flipped and a fair die is rolled. Find P(\text{Heads and a 4}).
Example 2
mediumFor two events A and B, P(A) = 0.4 and P(B) = 0.5. If A and B are independent, find (a) P(A \cap B) and (b) P(A \cup B).
Example 3
easyA student randomly guesses on two multiple-choice questions, each with 4 options. Find the probability of getting both correct.
Example 4
hardEvents A and B satisfy P(A) = 0.6, P(B) = 0.7, and P(A \cap B) = 0.42. Are A and B independent? Justify algebraically.