Please answer both multiple choice questions 1a and 1b. Please show all work and all steps.

1a.) The professor gives a random number of quizzes per week, in average 3 per week. What's the probability that this week you will have exactly 3 quizzes?

Multiple Choice. Choose ONE answer

a) 1 - e^(-4.5)

b) e^(-4.5)

c) e^(-3.5)

1b.) The professor gives a random number of quizzes per week, in average 3 per week. What's the probability that you'll have to wait more than 2 weeks until a week with 3 quizzes?

Multiple choice. Choose ONE answer

a) (1-e^(-4.5))^2

b) (1-e^(-3.5))^2

c) (e^(-9.5))^2