An article in Fire Technology, 2014 (50.3) studied the effectiveness of sprinklers in firecontrol 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. Assume the sprinklers activate correctly or not independently. (a) What is the probability that all of the sprinklers will operate correctly in a fire? Round your answer to three decimal places (e. g. 98.765)
(b) What is the probability that at least 7 of the sprinklers will operate correctly in a fire? Round your answer to two decimal places (e. g. 98.76),
(c) What is the minimum number of sprinklers needed so that the probability that at least one operates correctly is at least 0.98?