Is anyone able to help me with this question for my stats lab? Thanks

1. (16 points) Suppose I go to Tim Horton's to get a warm drink and a baked item. I choose at random and with equal probability one of coffee, tea or hot chocolate for the drink. I choose at random and with equal probability one of a muffin, a bagel or a donut for the baked item. (a) [2] List the sample space of all possible outcomes (that is, all possible combinations of 1 warm drink and 1 baked item). Use C, T and H to represent Coffee, Tea and Hot Chocolate and use M, B and D to represent Muffin, Bagel and Donut. (b) [5] List the outcomes in each of the following events: the drink is coffee or tea, i.e. P(C or T) (ii) the baked item is a bagel, i.e. P(B) the drink is coffee or tea, and the baked item is a bagel, i.e. P((C or T) and B) the drink is coffee or tea, or the baked item is a bagel, i.e. P((C or T) or B) 3 3 the drink is not tea or coffee, i.e. P(not (T or C)) (c) [5] Find the probability of each of the events in (b). Use 3 decimals in your answer, e.g., 0.123 (d) [2] Which of the following assumptions do you need to make about the drink choice and the baked item choice (select just 1)? Why is this assumption needed? They are independent (ii ) They are dependent (iii) They are complimentary (iv They are mutually exclusive (e) [2] In (b), are the events (i) and (ii) mutually exclusive? Explain why or why not