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Probability Pþease helpp

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Select numbers a and b between 0 and 1
independently and at random, and let c be their sum. Let A, B, and C be the results when a, b, and c, respectively, are rounded to the nearest integer. What is the probability that A + B = C?

  • Probability Pþease helpp - ,

    If a and b are decimals between 0 and 1, then
    A and B could be either 0 or 1
    The prob of a rounded up to 1 is 1/2 and
    the prob of a becoming 0 is 1/2

    forming a table:
    A B -----C
    0 0 ----- 0 e.g. .2+.1 = .3 --> 0
    0 0 ----- 1 e.g. .4 + .4 = .8 ---> 1 ...... FALSE
    0 1 ----- 1 e.g. .4 + .9 = 1.3 ---> 1
    1 0 ----- 1 e.g. .9+.4 = 1.3 --> 1
    1 1 ----- 1 e.g. .6 + .6 = 1.2 ---> 1 ... FALSE
    1 1 ----- 2 e.g. .9+.9 = 1.8 ---> 2

    I see 4 cases out of the 6 where A+B = C
    so prob = 4/6 = 2/3

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