Conditional Probability Worksheet
This worksheet focuses on understanding and calculating conditional probabilities for Grade 12 students, including real-world applications and Venn diagrams.
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Conditional Probability Worksheet
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Read each question carefully and show all your work. Round answers to three decimal places where appropriate.
1. In a study, 60% of students passed their math exam, and 40% of students passed their science exam. 30% of students passed both exams. What is the probability that a randomly selected student passed the math exam given that they passed the science exam?
2. A bag contains 5 red marbles and 3 blue marbles. If two marbles are drawn without replacement, what is the probability that the second marble drawn is blue, given that the first marble drawn was red?
3/8
3/7
5/8
5/7
3. If P(A|B) = 0.6, P(B) = 0.5, then P(A ∩ B) = .
4. Two events A and B are independent if P(A|B) = .
5. Consider the Venn diagram below showing the number of students who play soccer (S) and basketball (B).
a. What is the probability that a student plays soccer given that they play basketball?
b. What is the probability that a student plays basketball given that they play soccer?
6. For any two events A and B, P(A|B) = P(B|A).
True
False
7. A company manufactures light bulbs. It is known that 2% of the bulbs are defective. If a bulb is defective, there is a 95% chance that it will be detected by a quality control test. If a bulb is not defective, there is a 10% chance that it will be incorrectly identified as defective (false positive). What is the probability that a bulb is actually defective, given that the test identified it as defective?
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