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Question

(C) Let $x$ be the number of correct answers and $y$ be the number of incorrect answers.Total questions $x + y = 10$.Marks obtained $4x - y = 30$.Addi

Vedclass · Accepted Answer

$405$

Vedclass · Answer

(C) Let $x$ be the number of correct answers and $y$ be the number of incorrect answers.Total questions $x + y = 10$.Marks obtained $4x - y = 30$.Adding the two equations: $5x = 40 \implies x = 8$.Then $y = 10 - 8 = 2$.The probability of a correct answer is $p = 1/4$ and an incorrect answer is $q = 3/4$.The probability of getting $8$ correct and $2$ incorrect answers is given by the binomial distribution formula $P(X=8) = \binom{10}{8} p^8 q^2$.$P(X=8) = \binom{10}{2} (1/4)^8 (3/4)^2 = 45 	imes \frac{1}{4^8} 	imes \frac{9}{4^2} = \frac{45 	imes 9}{4^{10}} = \frac{405}{4^{10}}$.

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