Use the binomial probability distribution when your random variable is the number of successes on n success or failure trials when the probability of success, p , is the same for each trial, and the results of the trials are independent of each other, i.e. success on the rst trial doesn't change the probability of success on any other trial, etc. According to Chemical Engineering Progress (Nov. 1990) approximately 30% of all pipework failures in chemical plants are caused by operator error. (a) What is the probability that out of the next 3 pipework failures at least 2 are due to operator error? (b) What is the probability that out of the next 5 pipework failures at least 4 are due to operator error? (c) What is the probability that out of the next 10 pipework failures at least 9 are due to operator error