A committee will be formed with 4 managers and 3 engineers selected without An article in Fire Technology, 2014 {5&3} studied the effectiveness of sprinklers in re control by the number of sprinklers that activate correctly. The researchers estimate the probability of a sprinkler to activate correctly to be (LT. Suppose that you are an inspector hired to write a safety report for a large ballroom with III} sprinklers. Assume the sprinklers activate correctly or not independently. a. What is the probability that all the sprinklers will operate correctly in a re? b. What is the probability that at least it of the sprinklers will operate correctly in a re? c. What is the minimum number of sprinklers needed so that the probability that at least one operates correctly is at least 1199