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
Percentage Of messages server 1 server 2 server 3
Route 1 30 0.01 0.015
Route 2 70 0.02
0.003 (a) What is the probability that a message will arrive without error?
(b) If a message arrives in error, what is the probability it was sent through route 1?