Question 4: Imagine that you are eating at a restaurant with your friends. You and your best friend, Arabella, are seated at opposite ends of a large table, and Arabella orders first. The probability that both you and Arabella end up ordering vegetable soup is, in simpler terms, the probability that you order vegetable soup (P(A)) and the probability that Arabella orders vegetable soup (P(B)). This can be represented as P(A and B). The probability that you order vegetable soup given that you know Arabella has ordered it is. What is the probability that Arabella orders vegetable soup?
Question 5: Now suppose that your orders are independent of each other, and the probability that you order vegetable soup is. What is the probability that Arabella orders vegetable soup?