A website manager has noticed that during the evening hours, about 3 people per minute check out from their shopping cart and make an online purchase. She believes that each purchase is independent of others and assumes that the distribution of number of purchases per minute on the website follows Poisson distribution.
a. What is the probability that during a 1-minute period, at least two purchases are made?
b. What is the probability that no one makes a purchase in next 3 minutes?