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Math Help - easy discrete RV question

  1. #1
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    easy discrete RV question

    a grp of 4 components is known to have 2 defectives. a man tests the componets one at a time until the 2 are found. once he locates the 2 defectives, he stops testing, but the second defective is tested for accuracy. let Y denote the no. of test on which the second defective is found. find the prob distribution for Y.

    thanks!
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  2. #2
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    Rez
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    There are 3 possibilities for when he can find the first defective one: 1st, 2nd, or 3rd test.

    If he finds the first defective one on the 1st test, he can find the second on the 2nd, 3rd, or 4th test (3 possibilities).

    If he finds the first defective one on the 2nd test, he can find the second on the 3rd or 4th test (2 possibilities).

    If he finds the first defective one on the 3rd test, he can find the second on the 4th test only (1 possibility).

    So, there are 3 + 2 + 1 total ways for him to find the second defective component. For the probability distribution, how many of these ways involve him finding it on each test?
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