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Probability and byte

  1. Feb 14, 2007 #1
    1. The problem statement, all variables and given/known data

    In a binary communication system all bit bytes are possible, and equally likely. Any bit is equallly likely to be a 1 or 0.
    1- what is the probability of oberving a byte with exactly three 1's?
    2-if a byte is observed with exactly three i's, what is the probability the first bit is a 1?
    2. Relevant equations

    combination formula nCp

    3. The attempt at a solution

    1- I did:
    P(exactly three 1's)= C(3,8)/ 2^8

    Here I am confused:
    I did P( three 1's and 1 is first)=C(2,7)/(2^8)
    P(three 1's and 1 is first)=C(3,7)/(2^8)
    I cannot see which one is right.

    Can someone tell me what I did right and wrong?
    Thank you
    1. The problem statement, all variables and given/known data

    2. Relevant equations

    3. The attempt at a solution
  2. jcsd
  3. Feb 14, 2007 #2


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    Science Advisor
    Homework Helper

    2. Both your answers are wrong.

    If there you know 3 bits are 1, then the question is the same as "you have a bag with 3 black balls and 5 white balls, what is the probablilty that the first ball you take out is black".

    (If you can't see it, do the same problem with a 4-bit byte, and solve it by just writing out the 16 possibilities and counting them).
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