Question

For a certain binary communication channel, the probability a transmitted ‘0’ bit is received as a ‘0’ bit is 0.95 and for ‘1’ bit, it is 0.90. The probability that ‘0’ bit is transmitted is 0.4, Find

a. Probability that ‘1’ bit is received.

Answer 1

Let $A$ be the event of transmitting '1' and $\bar{A}$ be the event of transmitting '0'.

and $B$ be the event of receiving '1" and $\bar{B}$ be the event of receiving '0'.

a. Probability that ‘1’ bit is received-

$P(B)=P(A)P(\dfrac{B}{A})+P(\bar{A})P(\dfrac{B}{\bar{A}})$

$= 0.9\times (1-0.4)+0.4\times (1-0.95)\\[9pt]=0.6\times 0.9+0.4\times 0.05=0.56$