Question

2) An article in Fire Technology (2014) studied the effectiveness of sprinklers in fire control by the number of sprinklers that activate correctly. The researchers estimate the probability of a sprinkler to activate correctly to be 0.7. Suppose that you are an inspector hired to write a safety report for a large ballroom with 10 sprinklers. Let the random variable X denote the number of sprinklers in the ballroom that activate correctly. Assume the sprinklers activate correctly or not independently. (a) What is the probability mass function for X? (b) What is the probability that at least one sprinkler fails to operate correctly in a fire? (c) What is the probability that fewer than half of the sprinklers fail to operate? (d) What is the minimum number of sprinklers needed so that the probability that at least one operates correctly is at least 0.99?

Answer 1