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A congested computer network has a 0.006 probability of losing a data packet and packet losses are independent events. A lost packet must be resent. Round your answers to four decimal places (e.g. 98.7654) (a) What is the probability that an e-mail message with 100 packets wl need any resent? (b) What is the probability that an e-mail message with 3 packets will need exactly one to be resent? (c) If 10 e-mail messages are sent, each with 100 packets, what is the probability that at least one message will need some packets to be resent?

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Answer #1

a)P(need resend)=1-P(none of 100 need resend)=1-(0.994)100 =0.4522

b)P(exactly one resend)=3C1(0.006)1(0.994)2 =0.0178

c)P(at least one message need to be resend)=1-P(none of 10 have pakets to be resend)

=1-(0.994)1000 =0.9976

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