Refer to given Example, in which you and your friend Vanessa enter a drawing for a free lunch in Week 1 and again in Week 2. Events defined were A = you win in Week 1, B = Vanessa wins in Week 1, C = Vanessa wins in Week 2.
a. Are events B and C independent? Explain.
b. Suppose that after Week 1, the cards that were not drawn as the winning card are retained in the bowl for the drawing in Week 2. Are events B and C independent? Explain.
Example
Winning a Free Lunch Some restaurants display a glass bowl in which customers deposit their business cards, and a drawing is held once a week for a free lunch. The bowl is emptied after each week's drawing. Suppose that you and your friend Vanessa each deposit a card in 2 consecutive weeks. Define
Event A = You win in Week 1.
Event B = Vanessa wins in Week 1.
Event C = Vanessa wins in week 2.