3.31 The number of eggs a chicken hatches is a Poisson random variable. The probability that the chicken hatches no eggs is 0.10. What is the probability that she hatches at least two eggs? 3.33 Cars pass a busy intersection at a rate of approximately 16 cars per minute. What is the probability that at least 1000 cars will cross the intersection in the next hour? (Hint: What is the rate per hour?) 3.36 If you take the red pill, the number of colds you get next winter will have a Poisson distribution with  = 1. If you take the blue pill, the number of colds will have a Poisson distribution with  = 4. Each pill is equally likely. Suppose you get three colds next winter. What is the probability you took the blue pill? 3.37 A physicist estimated that the probability of a U.S. nickel landing on its edge is one in 6000. Suppose a nickel is flipped 10,000 times. Let X be the number of times it lands on its edge. Find the probability that X is between one and three using a) The exact distribution of X (b) An approximate distribution of X