It is observed that 25 % of the cases related | vedclass

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

Question

(B) The probability of a case being solved is $p = 25 \% = \frac{1}{4}$.Thus,the probability of a case not being solved is $q = 1 - p = \frac{3}{4}$.G

Vedclass · Accepted Answer

$\frac{19}{4096}$

Vedclass · Answer

(B) The probability of a case being solved is $p = 25 \% = \frac{1}{4}$.Thus,the probability of a case not being solved is $q = 1 - p = \frac{3}{4}$.Given $n = 6$ trials,we need to find the probability that at least $5$ cases are solved,which is $P(X \ge 5) = P(X = 5) + P(X = 6)$.Using the binomial distribution formula $P(X = x) = {}^nC_x p^x q^{n-x}$:$P(X = 5) = {}^6C_5 \left(\frac{1}{4}ight)^5 \left(\frac{3}{4}ight)^1 = 6 	imes \frac{1}{4^5} 	imes \frac{3}{4} = \frac{18}{4^6}$.$P(X = 6) = {}^6C_6 \left(\frac{1}{4}ight)^6 \left(\frac{3}{4}ight)^0 = 1 	imes \frac{1}{4^6} 	imes 1 = \frac{1}{4^6}$.Therefore,$P(X \ge 5) = \frac{18}{4^6} + \frac{1}{4^6} = \frac{19}{4^6} = \frac{19}{4096}$.

It is observed that $25 \%$ of the cases related to child labour reported to the police station are solved. If $6$ new cases are reported,then the probability that at least $5$ of them will be solved is

Similar Questions

Consider $5$ independent Bernoulli trials each with probability of success $p$. If the probability of at least one failure is greater than or equal to $\frac{31}{32}$,then $p$ lies in the interval:

$A$ man makes attempts to hit the target. The probability of hitting the target is $\frac{3}{5}$. Then the probability that he hits the target exactly $2$ times in $5$ attempts is:

In a workshop,there are five machines and the probability of any one of them to be out of service on a day is $\frac{1}{4}$. If the probability that at most two machines will be out of service on the same day is $\left(\frac{3}{4}\right)^{3} k$,then $k$ is equal to

During the winter months,in a certain village in Scotland,the probability of a day having severe fog is $0.6$. The probability that in a given week there will be exactly two days with severe fog is:

$A$ fair coin is tossed $n$ times. Let $X$ be the number of times head is observed. If $P(X = 4), P(X = 5)$ and $P(X = 6)$ are in $H.P.$,then $n$ is equal to

Vedclass Test Series

Exam Paper Generator

Online Exam Module