Question

A binary communication channel carries data as one of two sets of signals denoted by 0 (zero) and 1. Owing to noise, a transmitted 0 is sometimes received as a 1, and a transmitted 1 is sometimes received as a 0. For a given channel, it can be assumed that a transmitted 0 is correctly received with probability 0.95 and a transmitted 1 is correctly received with probability 0.75. Also, 70% of all messages are transmitted as a 0. If a signal is sent, determine the probability that a 1 was received.

Answer 1

26% probability that a 1 was received.

Explanation:

We have these following probabilities:

70% probability that a message is transmitted as a 0.

100 - 70 = 30% probability that a message is transmitted as a 1.

If a message is transmitted as a 0, 95% probability of being received as a 0 and 5% probability of being received as 1.

If a message is transmitted as a 1, 75% of being received as a 1 and 25% probability of being received as a 0.

If a signal is sent, determine the probability that a 1 was received.

5% of 70%(Sent 0, received 1) of 75% of 30%(sent 1 and received 1). So

`p = 0.05*0.7 + 0.75*0.3 = 0.26`

26% probability that a 1 was received.