Question

Question 7 2 pts Problems 7 and 8 pertain to the following situation. Three messages are sent across a channel. The probabilities of successful reception are.6.7 and.9 respectively. Assuming that the signals are all independent, find the probability of successfully receiving no signals: 0.68 O 0.12 0.012 0.378 0.456 Question 8 2 pts Three messages are sent across a channel. The probabilities of successful reception are.6.7 and.9 respectively. Assuming that the signals are all independent, find the probability of successfully receiving two signals only 1 0.456 0.378 0.12 1.59

Answer 1

    Let              
   A: event of receiving message A successfully              
   B: event of receiving message B successfully              
   C: event of receiving message C successfully              
   Hence compliments of the above events are              
   A': event of not receiving message A' successfully              
   B': event of not receiving message B' successfully              
   C': event of not receiving message C' successfully              
                  
   Given              
   P(A) = 0.6              
   P(B) = 0.7              
   P(C ) = 0.9              
                  
   Hence,              
   P(A') = 1 - P(A) = 1 - 0.6 = 0.4              
   P(B') = 1 - P(B) = 1 - 0.7 = 0.3              
   P(C') = 1 - P(C) = 1 - 0.9 = 0.1              
                  
                  
7)   To find P(successfully receiving no signals)              
   = P(A'B'C')              
   = P(A')*P(B')*P(C')              
   = 0.4*0.3*0.1              
   = 0.012              
                  
   Answer : Option 3              
   $\mathbf{\circ\ 0.012}$               
                  
                  
8)   To find P(successfully receiving two signals only)              
   = P(ABC' OR A'BC OR AB'C)              
   = P(ABC') + P(A'BC) + P(AB'C)              
   = 0.6*0.7*0.1 + 0.4*0.7*0.9 + 0.6*0.3*0.9              
   = 0.456              
                  
   Answer : Option 2              
     $\mathbf{\circ\ 0.456}$            

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