question_answer 65)

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 answer ‘true’, if it falls tails, he answers ‘true’, if it falls tails, he answer ‘false’. Find the probability that he answers at least 12 questions correctly. 

Answer:

Let x be the number of heads, then x has the binomial distribution with n = 20, p =  q = 1       Required probability = P       = P(x = 12) + P(x = 12) + ?. + P(x = 20)