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  • 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.

Q. 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.

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best_answer

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

The coin falls heads, he answers 'true'; if it falls tails, he answers 'false'. 

                         P=\frac{1}{2}      

                       q=1-P=1-\frac{1}{2}=\frac{1}{2}

X has a binomial distribution,n=20

                     \therefore \, \, \, \, P(X=x)=^nC_x.q^{n-x}.p^x

                             P(X=x)=^2^0C_x.(\frac{1}{2})^{20-x} . (\frac{1}{2})^{x}      

                              P(X=x)=^2^0C_x.   (\frac{1}{2})^{20}

P(at\, \, least\, 12\, \,questions \, \, answered\, \, correctly)=P(X\geq 12)

                                 =P(X=12)+P(X=13)..................+P(X=20)

                                =^{20}C_1_2 (\frac{1}{2})^{20}+^{20}C_1_3(\frac{1}{2})^{20}+..........^{20}C_2_0 (\frac{1}{2})^{20}

                               =(\frac{1}{2})^{20}(^{20}C_1_2 +^{20}C_1_3+..........^{20}C_2_0 )

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seema garhwal

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