A source transmits a message (a string if symbols). Each symbol is received inco

Question

A source transmits a message (a string if symbols). Each symbol is received incorrectly with probability 0.03. Assume that errors in symbol transmissions are independent. a. If a message containing 24 symbols is transmitted, what is the probability that at least one of the symbols is received incorrectly? b. If a message containing 30 symbols is transmitted, What is the probability that (exactly) 24 of the symbols is received correctly? c. A long message is transmitted. What is the probability that the 10^th symbol sent is the symbol that is received incorrectly?

Explanation / Answer

a) P(at least 1 incorrect symbol) = 1 - P(all correct symbols)

= 1 - 0.9730

= 0.599

b) P(24 correct symbols out of 30) = 30C24 x 0.9724 x 0.036

= 0.00021

c) P(10th symbol is the first incorrect symbol) = P(first 9 correct symbols and 10th incorrect symbol)

= 0.979 x 0.03

= 0.0228

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