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

Question

A source transmits a message (a string of 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 1^st symbol that is received incorrectly?

Explanation / Answer

a) probabilty at least one is with error =1-P(none is with error)=1-(1-0.03)24 =0.5186

b)probabilty =(1-0.03)30 =0.401

c) probabilty that 10th symbol is first one with error =P(first nine are flawless and 10th with error =0.979*0.03=0.0228

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