Tired of careless spelling and grammar, a company decides to administer a test to all job applicants. The test consists of 20 sentences. Applicants must state whether each sentence contains any grammar or spelling errors. Half the sentences contain errors. The company requires a score of 14 or more.
(a) If an applicant guesses randomly, what is the probability of passing?
(b) What minimum score would be required to reduce the probability of "passing by guessing" to 5 percent or less?