Answer Happy

3. Suppose we want to create a three-digit number. We are allowed to use the digits 0, 1, 3, 4, 6, 7, and 9. Each digit can be used only once, and a number starting with 0 is a considered a two-digit number. How many of these three-digit numbers are less than 450? 4. Suppose you have two events, A and B. Assume that P(A) = 0 and P(B) + 0. Is it possible for these events to be both mutually exclusive and independent at the same time? Provide a mathematical example illustrating your viewpoint. Your example should include • Definitions of the events A and B. Either start with them as mutually exclusive, or as independent of each other. When you are constructing these events, make sure they meet the criteria for one of mutually exclusive or independent. • The probability for A, and the probability for B. • If you started with A and B as mutually exclusive, provide a calculation to show if they are independent or not. • If you started with A and B as independent, provide a calculation to show if they are mutually exclusive or not.