Discussion Forum



1)

In a communication network , ninety eight precent of messages are transmitted with no error.If a random variable  X denotes the number of incorrectly transmitted messages , then the probability that atmost one message is transmitted incorrectly out of 500 messages sent, is


A) $\frac{11}{e^{10}}$

B) $\frac{e^{10}-1}{e^{10}}$

C) $\frac{10}{e^{10}}$

D) $\frac{98}{e^{10}}$

Answer:

Option A

Explanation:

Here,

 n=500 ,p=2%, q=98%

Required probability

 $P(X\leq1)=P(X=0)+P(X=1)$

 $=\frac{\lambda^{0}e^{-\lambda}}{0!}+\frac{\lambda^{}e^{-\lambda}}{1!}$

  $P(X\leq1)=e^{-\lambda}(1+\lambda)$

 = $e^{-10}(1+10)$                   [$\because  \lambda=np= 500 \times \frac{2}{100}=10$]

= $\frac{11}{e^{10}}$