An e-mail message can travel through one of two server routes. The probability of transmission error in each of the servers and the proportion of messages that each route are shown in the following table. Assume that the servers are independent. Probability of Error Route 1 Route 2 Percentage of Messages 35 P = 65 Server 1 0.01 Server 2 Server 3 Server 4 0.015 0.02 0.003 (a) What is the probability that a message will arrive without error? Round your answer to four decimal places (e.g. 98.7654).

A First Course in Probability (10th Edition)
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Chapter1: Combinatorial Analysis
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An e-mail message can travel through one of two server routes. The probability of transmission error in each of the servers and the proportion of messages that travel
each route are shown in the following table. Assume that the servers are independent.
Probability of Error
Route 1
Route 2
P =
Percentage
of
Messages
35
65
P =
Server 1
0.01
Server 2 Server 3 Server 4
0.015
0.02
(a) What is the probability that a message will arrive without error?
Round your answer to four decimal places (e.g. 98.7654).
0.003
(b) If a message arrives in error, what is the probability it was sent through route 1?
Round your answer to four decimal places (e.g. 98.7654).
Transcribed Image Text:An e-mail message can travel through one of two server routes. The probability of transmission error in each of the servers and the proportion of messages that travel each route are shown in the following table. Assume that the servers are independent. Probability of Error Route 1 Route 2 P = Percentage of Messages 35 65 P = Server 1 0.01 Server 2 Server 3 Server 4 0.015 0.02 (a) What is the probability that a message will arrive without error? Round your answer to four decimal places (e.g. 98.7654). 0.003 (b) If a message arrives in error, what is the probability it was sent through route 1? Round your answer to four decimal places (e.g. 98.7654).
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