1. (a) An engineer tests 20 light bulbs, each with a 0.05 probability of being defective. What the probability that exactly 2 light bulbs are defective. (7 marks) (b) A random variable X has a Poisson distribution with parameter λ such that P (X = 1) = (0.2) P (X = 2). Find P (X = 0). (8 marks) 2. Data was collected on bolt failures in tower anchors. A large number of anchor assemblies, each with the same number of bolts, were tested to find out whether each bolt was a success or a failure. The number of passing bolts in an assembly had a mean value of 3.5 and a variance of 1.05. If failing bolts occur randomly and independently, find the probabilities associated with possible numbers of passing bolts in an assembly. An assembly is considered adequate if there is one or fewer bolt failures, what is the probability that a randomly chosen assembly will be inadequate? (15 marks)