SOLUTION: In a binary communication system a zero and a one is transmitted with probability 0.6 and 0.4 respectively. Due to error in the communication system a zero becomes a one with a pro

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Question 1194186: In a binary communication system a zero and a one is transmitted with probability 0.6 and 0.4 respectively. Due to error in the communication system a zero becomes a one with a probability 0.1 and a one becomes a zero with a probability 0.08. Determine the probability (i) of receiving a one and (ii) that a one was transmitted when the received message is one
Answer by ikleyn(52858)   (Show Source): You can put this solution on YOUR website!
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In a binary communication system a zero and a one is transmitted with probability 0.6 and 0.4 respectively.
Due to error in the communication system a zero becomes a one with a probability 0.1 and a one becomes
a zero with a probability 0.08. Determine the probability
(i) of receiving a one and
(ii) that a one was transmitted when the received message is one
~~~~~~~~~~~~~~~ 

(i)  P(receiving a one) = P(posting a zero)*P(zero becomes a one) + P(posting a one)*P(one remains one) = 

                                        0.6*0.1                   +              0.4*(1-0.08)           = 0.428.   ANSWER



(ii) In this part, the problem asks about the conditional probability of transmitting one given that received 

     message is one.  So, the denominator of the conditional fraction is   P(receiving a one) = 0.428, just founded 

     in part (i).


     The numerator of this fraction for conditional probability is   

          P(posting a one)*P(one remains one)  = 0.4*(1-0.08) = 0.368.  


     Thus the final  ANSWER  for this part is  P =  = 0.8598  (rounded).

Solved.



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