One evening at a local restaurant, a manager decided to ask his patrons which meals they had cooked for themselves during the day, as opposed to eating out at a restaurant.

Question

The manager found that 30% cooked breakfast, 20% cooked lunch, and 7% cooked both meals. (Round to 2 decimal places, if needed)

a) What is the probability that a randomly selected patron cooked breakfast or lunch?

b) What is the probability that a randomly selected patron cooked breakfast but not lunch?

c) What is the probability that a randomly selected patron cooked lunch but not breakfast?

d) What is the probability that a randomly selected patron cooked none of their meals?

Answer 1

A = cook breakfast (0.30)

B = cook lunch (0.20)

A an B = 0.07

a) What is the probability that a randomly selected patron cooked breakfast or lunch?

P(A or B) = P(A) + P(B) - P(A and B) = 0.3 + 0.2 = 0.07 = 0.43

b) What is the probability that a randomly selected patron cooked breakfast but not lunch?

P(A and not B) = P(A) - P(A and B) = 0.3 - 0.07 = 0.23

c) What is the probability that a randomly selected patron cooked lunch but not breakfast?

P(B and not A) = P(B) - P(A and B) = 0.2 - 0.07 = 0.13

d) What is the probability that a randomly selected patron cooked none of their meals?

P(not (A or B)) = 1 - P(A or B) = 1 - 0.43 = 0.57