To communicate one bit of information reliably, cellular phones transmit the same binary symbol five times. Thus the information “zero” is transmitted as 00000 and “one” is 11111. The receiver detects the correct information if three or more binary symbols are received correctly. What is the information error probability P[E] , if the binary symbol error probability is q = 0.1?

A First Course in Probability (10th Edition)
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Chapter1: Combinatorial Analysis
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Please solve using Bayes' Theorem:

To communicate one bit of information reliably, cellular phones transmit the same binary symbol five times. Thus the information “zero” is transmitted as 00000 and “one” is 11111. The receiver detects the correct information if three or more binary symbols are received correctly. What is the information error probability P[E] , if the
binary symbol error probability is q = 0.1?

 

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