A multiple choice examination has 5 questions | vedclass

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

Question

(C) Let $n = 5$ be the total number of questions. Since each question has $3$ alternatives with only $1$ correct,the probability of success $p = \frac

Vedclass · Accepted Answer

$\frac{11}{243}$

Vedclass · Answer

(C) Let $n = 5$ be the total number of questions. Since each question has $3$ alternatives with only $1$ correct,the probability of success $p = \frac{1}{3}$ and the probability of failure $q = 1 - \frac{1}{3} = \frac{2}{3}$. We use the binomial distribution formula $P(X = k) = {}^nC_k p^k q^{n-k}$. We need to find the probability of getting $4$ or more correct answers,which is $P(X \geq 4) = P(X = 4) + P(X = 5)$. $P(X = 4) = {}^5C_4 \left(\frac{1}{3}ight)^4 \left(\frac{2}{3}ight)^1 = 5 	imes \frac{1}{81} 	imes \frac{2}{3} = \frac{10}{243}$. $P(X = 5) = {}^5C_5 \left(\frac{1}{3}ight)^5 \left(\frac{2}{3}ight)^0 = 1 	imes \frac{1}{243} 	imes 1 = \frac{1}{243}$. Therefore,$P(X \geq 4) = \frac{10}{243} + \frac{1}{243} = \frac{11}{243}$.

$A$ 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 $4$ or more correct answers just by guessing is

Similar Questions

The probability that a student is not a swimmer is $\frac{1}{5}$. What is the probability that out of $5$ students,$4$ are swimmers?

The mean and the variance of a binomial distribution are $4$ and $2$ respectively. Then the probability of $2$ successes is

$A$ and $B$ are playing a chess game with each other. The probability that $A$ wins the game is $0.6$,the probability that he loses is $0.3$,and the probability that it is a draw is $0.1$. If they play three games,what is the probability that $A$ wins at least two games?

$A$ discrete random variable $X$ has the distribution $B(15, p)$. Given that $\operatorname{Var}(X) = 3.15$. Then,the two possible values of $p$ are

The minimum number of times a fair coin needs to be tossed so that the probability of getting at least two heads is at least $0.96$ is:

Vedclass Test Series

Exam Paper Generator

Online Exam Module