Ex 13.5, 7 - Chapter 13 Class 12 Probability

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Ex 13.5, 7 In an examination, 20 questions of true-false type are asked. Suppose a student tosses a fair coin to determine his answer to each question. If the coin falls heads, he answers 'true'; if it falls tails, he answers 'false'. Find the probability that he answers at least 12 questions correctly. Let X : be the number of questions he answers correctly Tossing a coin is a Bernoulli trial So, X has binomial distribution P(X = x) = nCx n = number of questions = 10 p = Probability of getting answer correct Since it is a true false question P(he answers correctly) = p = 1 2 q = 1 p = 1 1 2 = 1 2 Hence, P(X = x) = 20Cx 1 2 1 2 20 P(X = x) = 20Cx 1 2 20 + P(X = x) = 20Cx We need to find probability that he answers at least 12 questions correctly i.e. P(X 12) P(X 12) = P(12) + P(13) + P(14) + .. +P(20) = 20C12 1 2 20 + 20C13 1 2 20 + 20C14 1 2 20 + + 20C20 1 2 20 = (20C12 + 20C13 + 20C14 + .. + 20C20)