Question

A faulty communication line for digital signals flips 25% of the 0's to 1's and 1/3 of the 1's to 0's. if 40% of a particular file being transmitted consists of 0's and 60% consists of 1's, what is the probability that when a 0 is received it was transmitted correctly (i.e., a 0 was transmitted)?

Answer 1

I find it helpful to put the given information into a chart. It shows the probability of receiving a 0 is 50%, and that when a 0 is received, 30% of the time a 0 was sent and 20% of the time a 1 was sent.

Hence ...

P(sent 0 | received 0) = P(sent 0 & received 0) / P(received 0)

P(sent 0 | received 0) = 0.30/0.50 = 3/5 = 0.60