SOLUTION: An n-byte message is being sent. For greater reliability, k independent information transmission channel is used. What is the probability that at least one channel receives an und

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Question 1200587: An n-byte message is being sent. For greater reliability, k independent information transmission channel is used.
What is the probability that at least one channel receives an undistorted message if the probability of a byte being scrambled on each channel is p? (p = 0.23, n = 9, k = 3)
Answer by ikleyn(52776) About Me  (Show Source):
You can put this solution on YOUR website!
.
An n-byte message is being sent. For greater reliability, k independent information
transmission highlight%28cross%28channel%29%29 channels highlight%28cross%28is%29%29 are used.
What is the probability that at least one channel highlight%28cross%28receives%29%29 transmits
an undistorted message if the probability of a byte being highlight%28cross%28scrambled%29%29
spoiled/(corrupted) on each channel is p? (p = 0.23, n = 9, k = 3).
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        Wording is definitely curved and oblique in this post. 


The probability of the 9-bite message to be undistorted in all 9 bites by any one 
of k=3 independent information transmission channels is

    p = %281-p%29%5En = %281-0.23%29%5E9 = 0.77%5E9 = 0.09515 (rounded).


With k=3 independent information transmission channels the probability to transmit
at least one undistorted message is 

    P = 1+-+%281-p%29%5E3 = 1+-+%281-0.09515%29%5E3 = 0.25915  (rounded).    ANSWER

Solved.