Q80 / 160 · TS EAMCET 2019 (03 May Shift 2) · Mathematics

In a communication network, ninety-eight percent 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

  • Correct answer
    A
    11e10
  • B
    e10-1e10
  • C
    e10
  • D
    98e10

Solution

n=500, q=98%=98100

Also, p+q=1

⇒p=2100

P(r≤1)=P(r=0)+P(r=1)

As per Poisson's distribution,

P(X=r)=λxe-λX!

Now, P(r≤1)=λ0e-λ0!+λ1e-λ1!

=e-λ(1+λ)

Also, λ=np=500×2100=10

So, P(r≤1)=e-10·(1+10)=11e10

Hence, the correct answer is option: 'A'.

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