A student writes an examination which contain | vedclass

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

Question

(D) The total number of questions is $n = 8$. Since each question is true or false,the probability of answering correctly is $p = \frac{1}{2}$ and inc

Vedclass · Accepted Answer

$\frac{219}{256}$

Vedclass · Answer

(D) The total number of questions is $n = 8$. Since each question is true or false,the probability of answering correctly is $p = \frac{1}{2}$ and incorrectly is $q = \frac{1}{2}$.Let $X$ be the number of correct answers. $X$ follows a binomial distribution $B(8, \frac{1}{2})$.The student passes if $X \ge 6$.$P(	ext{Pass}) = P(X=6) + P(X=7) + P(X=8)$$P(	ext{Pass}) = \binom{8}{6}(\frac{1}{2})^8 + \binom{8}{7}(\frac{1}{2})^8 + \binom{8}{8}(\frac{1}{2})^8$$P(	ext{Pass}) = \frac{28 + 8 + 1}{256} = \frac{37}{256}$.The probability that the student fails is $P(	ext{Fail}) = 1 - P(	ext{Pass})$.$P(	ext{Fail}) = 1 - \frac{37}{256} = \frac{219}{256}$.

$A$ student writes an examination which contains $8$ true or false questions. If he answers $6$ or more questions correctly,he passes the examination. If the student answers all the questions,then the probability that he fails in the examination is

Similar Questions

$A$ fair coin is tossed $100$ times. The probability of getting tails an odd number of times is

If $X \sim B(5, p)$ is a binomial variate such that $P(X=3)=P(X=4)$,then $P(|X-3| < 2)=$

$7$ coins are tossed simultaneously and the number of heads turned up is denoted by the random variable $X$. If $\mu$ is the mean and $\sigma^2$ is the variance of $X$,then $\frac{\mu \sigma^2}{P(X=3)}=$

The probability that a person who undergoes a certain operation will survive is $0.2$. If $5$ patients undergo similar operations,then the probability that exactly four will survive is

Vedclass Test Series

Exam Paper Generator

Online Exam Module