In a multiple-choice examination, there are 1 | vedclass

Name: Exam Paper Generator | JEE NEET Paper Generator | Vedclass
Brand: Vedclass
Rating: 5 (35 reviews)

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 $P(X=8) = \binom{10}{8} p^8 q^2$.$P(X=8) = \binom{10}{2} (1/4)^8 (3/4)^2 = 45 	imes \frac{1}{4^8} 	imes \frac{9}{4^2} = \frac{45 	imes 9}{4^{10}} = \frac{405}{4^{10}}$.

Similar Questions

An unbiased die is tossed $500$ times. The standard deviation of getting sixes in these $500$ tosses is

If getting a head on a coin when it is tossed is considered as success, then the probability of having more number of failures when ten fair coins are tossed simultaneously is

Four fair dice are thrown independently $27$ times. Then the expected number of times,at least two dice show up a $3$ or a $5$ is

If the mean and variance of a binomial distribution are $\frac{4}{3}$ and $\frac{10}{9}$ respectively, then $P(X \geq 6)=$

If $8$ coins are tossed simultaneously,then the probability of getting at least $6$ heads is

Vedclass Test Series

Exam Paper Generator

Online Exam Module