You’re designing a new ultra low power digital wireless communication device. Du

Question

You’re designing a new ultra low power digital wireless communication device. During testing of you’re prototype, you observe that 55% of bits sent are 1’s and 45% of bits sent are 0’s. If a 1 is sent, the probability of an error is 0.17. If a 0 is sent, the probability of an error is 0.09. Assume the transmission of each bit is an independent event and that the errors are also independent given the true values of the bits that were sent.

So, the Question is What is the probability of no errors in a string of 8 bits making up a randomly selected integer?

Explanation / Answer

For 1 bit,

P(No error) = P(No error | bit is 1) * P(bit is 1) + P(No error | bit is 0) * P(bit is 0) = (1-0.17)*0.55 + (1-0.09)*0.45

= 0.866

No error in 8 bits = 0.8668 = 0.3163

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