The number of emails that I get in a weekday (Monday throughFriday) can be modeled by a Poisson distribution with an average of1/6 emails per minute. The number of emails that I receive onweekends (Saturday and Sunday) can be modeled by a Poissondistribution with an average of 1/30 emails per minute.

What is the probability that I get no emails in an interval oflength 4 hours on a Sunday?

A random day is chosen (all days of the week are equally likelyto be selected), and a random interval of length one hour isselected on the chosen day. It is observed that I did not receiveany emails in that interval. What is the probability that thechosen day is a weekday?