A congested computer network has a 0.005 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 will 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?

Question

Elliot Matthews

Engineering

17 November, 12:30

A congested computer network has a 0.005 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 will 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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Answers (1)

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Starr · Answer 1

Answer

given,

Probability of loosing data, p = 0.005

q = 1 - 0.005 = 0.995

a) Probability that none of the need resent in the 100 Pack

= ¹⁰⁰C₀ p⁰q¹⁰⁰

= 0.995¹⁰⁰ = 0.6057

Probability at least one mail is resent = 1 - 0.6057

= 0.3942

b) Probability that that exactly one out of three needs to be resent is:

= ³C₁ p¹q²

= 3 x 0.005 x 0.995²

= 0.0149

c) Probability that none of the need resent in the 1000 Pack

= ¹⁰⁰⁰C₀ p⁰q¹⁰⁰⁰

= 0.995¹⁰⁰⁰ = 0.006657

Probability at least one mail is resent = 1 - 0.006657

= 0.9933