Independent and Dependent Events Worksheet

Independent and Dependent Events

Read each question carefully and answer to the best of your ability. Show all work where applicable.

1. Which of the following describes two events where the outcome of the first event does NOT affect the outcome of the second event?

2. A bag contains 3 red marbles and 2 blue marbles. If you draw a marble, replace it, and then draw another marble, what type of events are these?

3. The probability of two independent events A and B both occurring is given by P(A and B) = P(A)   P(B).

4. If two events are dependent, the probability of both occurring is P(A and B) = P(A)   P(B|A).

5. A standard deck of 52 cards is used. What is the probability of drawing a King, not replacing it, and then drawing another King?

6. A coin is flipped and a standard six-sided die is rolled. What is the probability of getting a 'Heads' on the coin and a '4' on the die?

7. Drawing a card from a deck, replacing it, and then drawing another card are dependent events.

8. The probability of two independent events occurring is always greater than the probability of either event occurring alone.

9. A box contains 4 green pens and 6 blue pens. You pick a pen, do NOT replace it, and then pick another pen. What is the probability that both pens are blue?

10. In a class, 60% of students study Math and 40% study Physics. If 25% of students study both Math and Physics, are the events 'studying Math' and 'studying Physics' independent? Justify your answer.