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  1. Consider a Binary Symmetric Channel (BSC) with probability of error being p. To transmit a bit, say 1, we transmit a sequence of three 1 s. The receiver will interpret the received sequence to represent 1 if at least two bits are 1. The probability that the transmitted bit will be received in error is

    2. A.
    p3 + 3p2 (1 - p)
    B.
    p3
    C.
    (1 - p)3
    D.
    p3 + p2 (1 -p)

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    Answer : Option A

    Explanation :

    Probability of error = P

    Thus probability of no error = (1 - P)

    Now probability that transmitted bit, received in error

    = all bits are with error + one bit is with error

    = P3 + 3C1P2 (1 - P) = P3 + 3P2 (1 - P).

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