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Problem 4: The number of times that a customer experiences a system failure in a given year is a Poisson random variable with parameter \lambda = 3. A new software patch has just been released that reduces the Poisson parameter to \lambda = 2 for 75 percent of users. For the other 25 percent, the patch has no appreciable effect on system failures. If a customer installs the patch and experiences 0 system failures in a year, how likely is it that the patch is effective for this customer? Problem 5: An urn contains 50 marbles (35 green and 15 white). a) 15 marbles are selected without replacement. Find the probability that exactly 10 out of 15 selected are green. b) 2 marbles are selected without replacement. Find the probability that 1 green and 1 white is obtained. c) Can you solve part (b) by using binomial distribution?