Question

From previous experience we know that probability of a sprinkler to activate correctly to be 0.7. I am going to inspect 10 sprinklers. Assume the sprinklers activate correctly or not

independently. (a) What is the probability that all of the sprinklers will operate correctly? (b) What is the probability that at least 7 of the sprinklers will operate correctly? (c) What is the minimum number of sprinklers needed so that the probability that at least one operates correctly is at least 0.99?

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