Suppose that in a dial-up connection you may be connected through one of three t

Question

Suppose that in a dial-up connection you may be connected through one of three types of channels with varying quality of transmission. In Type I the channel has an error probability of 0.01, in Type II the channel has an error probability of 0.005, and in Type III the channel has an error probability of 0.001. Suppose we assume that for the service provider used, 20% of the channels are of Type I, 30% of the channels are of Type II and 50% of the channels are of Type III.

a. What is the probability of error for an arbitrary connection?

b. Suppose we observe an error, what is the probability that we were connected via a channel Type I?

Explanation / Answer

a)probability of error for an arbitrary connection =P(connection I and error +connection II and error +connection III and error ) =0.2*0.01+0.3*0.005+0.5*0.001=0.004

b)  probability that we were connected via a channel Type I ; given observe an error

=P(connection I and error)/P(observe an error ) =0.2*0.01/0.004 =0.5

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