2. Of all people who enter Rooster’s Coffeehouse, 79% order a beverage, 53% order food, and 45% orderboth a beverage and food.

(a) You plan to select one customer at random. Explicitly define the two events that could occur. Express each of the three probabilities listed above as the probability in terms of these two events.

Note: For each part in the remainder of this question, you must first express each probability in terms of the events you defined in part (a) and justify any computation through the use of a formula.

(b) Are ordering a beverage and ordering food mutually exclusive events? Explain using only one of the probabilities you stated in part (a).

(c) What is the probability that a customer does not order food?

(d) What proportion of all people ordered a beverage, food, or both?

(e) What proportion of people order no beverage and no food? (HINT: How does this relate to part (d)?) erage and no food? (HINT: How does this relate to part (d)?)