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  • On a multiple choice examination with three possible answers for each of the five questions, what is the probability that a candidate would get four or more correct answers just by guessing?

Q. 9   On a multiple choice examination with three possible answers for each of the five questions, what is the probability that a candidate would get four or more correct answers just by guessing ?

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Let X represent number of correct answers by guessing in set of 5 multiple choice questions.

 Probability of getting a correct answer :

                                                                P=\frac{1}{3}

                                               \therefore q=1-P=1-\frac{1}{3}=\frac{2}{3}

X has a binomial distribution,n=5.

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

                P(X=x)=^5C_x.(\frac{2}{3})^{5-x} . (\frac{1}{3})^{x}

              P(guessing \, \, more\, \, than \, 4\, correct\, answer)=P(X\geq 1)

                                                                                                        =P(X=4)+P(X=5)

                                                                                                          =^5C_4.(\frac{2}{3})^{1} . (\frac{1}{3})^{4}+^5C_5(\frac{2}{3})^{0} . (\frac{1}{3})^{5}

                                                                                                          =\frac{10}{243}+\frac{1}{243}

                                                                                                          =\frac{11}{243}

Posted by

seema garhwal

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