In all of the probability problems studied so far, the events were independent. Events are independent when one event does not affect the outcome of the next event. In many probability problems, however, the outcome of one event does affect the outcome of other events. The following exercise will be used to help you better understand dependent and independent events. In this exercise, there are two bags, labeled Bag A and Bag B, each containing five marbles. Each bag has three red and two white marbles. In the exercise, the marbles will be drawn from the bags one marble at a time. The marble drawn from Bag A will be replaced after each draw. The marble from Bag B will not be replaced after each draw. 1. The first marble is drawn from Bag A. The probability that a red marble will be drawn is: A) B) : C) B D) 3 2. The first marble is drawn from Bag B. The probability that a red marble will be drawn is: A) B- B) : C) 3 D) 3 3. For the second draw, Bag A will have: A) 2 marbles B) 4 marbles C) 5 marbles D) 1 marble 4. For the second draw, Bag B will have: A) 2 marbles B) 4 marbles C) 5 marbles D) 1 marble In answering the following questions, it is important to know that a red marble was drawn from both bags in the first draw. 5. For the second draw, the probability that a red marble will be drawn from Bag A is: A) ? B) C) 3 D) : 6. For the second draw, the probability that a white marble will be drawn from Bag A is: A ) : B) ? C) D) 7. For the second draw, the probability that a red marble will be drawn from Bag B is: A) 3 B) 4 C) D) 3 8. For the second draw, the probability that a white marble will be drawn from Bag B is: A) B) 4 C) 2 D) 3 In answering the following questions, it is important to know that on the second draw, a red marble was drawn from Bag A and a white marble was drawn from Bag B. 9. For the third draw, the probability that a red marble will be drawn from Bag A is: A) 3 B) B C) D) : 10. For the third draw, the probability that a white marble will be drawn from Bag A is: A) B) ? C) ? D) ? 11. For the third draw, the probability that a red marble will be drawn from Bag B is: A) 3 B) 3 C) 2 D) +