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Question

In a 20-question true-false examination, suppose a student tosses a fair coin to determine his answer to each question. For every head, he answers 'true' and for every tail, he answers 'false'. Find the probability that he answers at least 12 questions correctly.


Solution

Let X denote the number of correct answers.
Then, X follows a binomial distribution with n =20

Let p be the probability of a correct answer. p= getting a head and a right answer to be true or getting a tail and a right answer to be falsep= 12 q=1- 12=12Hence, the distribution is given byP(X=r) = Cr2012r1220-r   , r=0,1,2,3......20= Cr20220Probability that the student answers at least 12 questions correctly=P(X12) = P(X=12)+P(X=13)+...+P(X=20)= C1220+C1320+...+C2020220

Mathematics
RD Sharma XII Vol 2 (2015)
Standard XII

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