Communication through a noisy channel. A source transmits a message (a string of symbols) through a noisy communication channel. Each symbol is 0 or 1 with probability p and 1−p, respectively, and is received incorrectly with probability ε0 and ε1, respectively. Errors in different symbol transmissions are independent.
a. What is the probability that the kth symbol is received correctly?
b. What is the probability that the string of symbols 1011 is received correctly?
c. In an effort to improve reliability, each symbol is transmitted three times and the received string is decoded by majority rule. In other words, a 0 (or 1) is transmitted as 000 (or 111, respectively), and it is decoded at the receiver as a 0 (or 1) if and only if the received three-symbol string contains at least two 0s (or 1s, respectively). What is the probability that a 0 is correctly decoded?
d. For what values of ε0 is there an improvement in the probability of correct decoding of a 0 when the scheme of part (c) is used?
e. Suppose that the scheme of part (c) is used. What is the probability that a symbol was 0 given that the received string is 101?

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Hi Clough
No, I wanted some help to come up with the answers myself and then check then check the answers to see if it's right..

Thanks

For
a: I got " p(1-e0)+ (1-p)(1-e1)"
Is it right?

out of (2n+1) tickets consecutively numbered, three are drawn at random. Find the chance that the numbers are in A.P