In a binary communication channel, the probability that a transmitted zero is received as zero is 0.95 and the probability that a transmitted one is received as one is 0.90. if the probability that zero is transmitted is 0.4, then what is the probability that a one was transmitted, given that a one was received?
the probability that 0 is transmitted = 0.4
therefore the probability that 1 is transmitted = 1-0.4 = 0.6
the probability that 0 is transmitted and 1 is received = 0.4*(1-0.95)
=0.4*0.05
=0.02
the probability that 1 is transmitted and 1 is received = 0.6*0.9
=0.54
therefore the probability that 1 is received = 0.02+0.54
= 0.56
thus the probability that 1 is transmitted , given that 1 is received
= 0.54/ 0.56
= 27/28
hope this helps you
therefore the probability that 1 is transmitted = 1-0.4 = 0.6
the probability that 0 is transmitted and 1 is received = 0.4*(1-0.95)
=0.4*0.05
=0.02
the probability that 1 is transmitted and 1 is received = 0.6*0.9
=0.54
therefore the probability that 1 is received = 0.02+0.54
= 0.56
thus the probability that 1 is transmitted , given that 1 is received
= 0.54/ 0.56
= 27/28
hope this helps you