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. - Mathematics

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.

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Solution

Let X represent the number of correctly answered questions out of 20 questions.

The repeated tosses of a coin are Bernoulli trails. Since “head” on a coin represents the true answer and “tail” represents the false answer, the correctly answered questions are Bernoulli trials.

`:. p = 1/2`

`:. q =1 - p = 1-1/2 = 1/2`

X has a binomial distribution with n = 20 and p = 1/2