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Math Help - [SOLVED] Probability

  1. #1
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    [SOLVED] Probability

    Kaplan Page 136 #23

    at a certain factory 5/8 of the workers are married and 3/4 are at least 40 years old. if 1/4 of the married workers are younger than 40, what fraction of the workers who are at least 40 are not married?

    The answer is 3/8 Why?

    Thanks in advance
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  2. #2
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    Try drawing a venn diagram with 2 overlapping circles; one for married and one for at least 40yo.

    You know:
    P(married) = 5/8.
    P(at least 40yo) = 3/4.
    P(married \cap less than 40yo) = 1/4.

    So P(married) = P(married \cap at least 40yo) + P(married \cap less than 40yo)
    5/8 = P(married \cap at least 40yo) + 1/4

    P(married \cap at least 40yo) = 5/8 - 1/4 = 3/8
    P(at least 40yo) = P(married \cap at least 40yo) + P(not married \cap at least 40yo)
    3/4 = 3/8 + P(not married \cap at least 40yo)

    Therefore, P(not married \cap at least 40yo) = 3/4 - 3/8 = 3/8
    Last edited by nzmathman; December 4th 2008 at 06:32 PM. Reason: made a minor mistake
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