Conditional Probability Worksheet

Conditional Probability Worksheet

Read each question carefully and answer to the best of your ability. Show all your work for full credit.

1. 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?

2. In a class, 60% of students study Math and 40% study Science. If 20% of students study both Math and Science, what is the probability that a randomly selected student studies Science given that they study Math?

3. The formula for conditional probability P(A|B) is P(A ∩ B) / P( ).

4. If two events A and B are independent, then P(A|B) = P( ).

5. A standard deck of 52 cards is used. What is the probability that a randomly drawn card is a King, given that it is a face card?

6. A family has two children. What is the probability that both children are girls, given that at least one of them is a girl?

Use the Venn Diagram below to answer the following questions.

7. Find P(A).

8. Find P(B).

9. Find P(A|B).

10. Find P(B|A).

11. If P(A|B) = P(A), then events A and B are independent.

12. Conditional probability is always less than or equal to the probability of the conditioned event.