A multiple choice examination has 5 questions. Each question has three alternative answers of which

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14.Probability

medium

A multiple choice examination has $5$ questions. Each question has three alternative answers of which exactly one is correct. The probability that a student will get $4$ or more correct answers just by guessing is :

A

$\frac{{17}}{{{3^5}}}$

B

$\;\frac{{13}}{{{3^5}}}$

C

$\;\frac{{11}}{{{3^5}}}$

D

$\;\frac{{10}}{{{3^5}}}$

(JEE MAIN-2013)

Solution

$p=\frac{1}{3}, q=\frac{2}{3}$

$^{5} \mathrm{C}_{4}\left(\frac{1}{3}\right)^{4} \cdot \frac{2}{3}+^{5} \mathrm{C}_{5}\left(\frac{1}{3}\right)^{5}$

$=5 \cdot \frac{2}{3^{5}}+\frac{1}{3^{5}}=\frac{11}{3^{5}}$

Standard 11

Mathematics

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