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

Question

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, 11 e 10, e 10 - 1 e 10, e 10, 98 e 10

MARKS App · Accepted Answer

n = 500 , q = 98 % = 98 100 Also, p + q = 1 ⇒ p = 2 100 P ( r ≤ 1 ) = P ( r = 0 ) + P ( r = 1 ) As per Poisson's distribution, P ( X = r ) = λ x e - λ X ! Now, P ( r ≤ 1 ) = λ 0 e - λ 0 ! + λ 1 e - λ 1 ! = e - λ ( 1 + λ ) Also, λ = n p = 500 × 2 100 = 10 So, P ( r ≤ 1 ) = e - 10 · ( 1 + 10 ) = 11 e 10

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