A multiple choice examination has 5 questions | vedclass

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Question

(D) There are $5$ questions and each question has $3$ options of which one is correct. Probability of getting a correct answer for any question is $p

Vedclass · Accepted Answer

$\frac{211}{243}$

Vedclass · Answer

(D) There are $5$ questions and each question has $3$ options of which one is correct. Probability of getting a correct answer for any question is $p = \frac{1}{3}$. Probability of getting an incorrect answer is $q = 1 - p = 1 - \frac{1}{3} = \frac{2}{3}$. We need to find the probability of getting at least one correct answer. $P(	ext{at least one correct}) = 1 - P(	ext{none correct})$. The probability that none of the $5$ questions are answered correctly is given by $P(X=0) = {}^{5}C_{0} 	imes p^{0} 	imes q^{5}$. $P(X=0) = 1 	imes 1 	imes (\frac{2}{3})^{5} = \frac{32}{243}$. Therefore,$P(	ext{at least one correct}) = 1 - \frac{32}{243} = \frac{243 - 32}{243} = \frac{211}{243}$.

$A$ 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 at least one correct answer is

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