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Probability Distribution

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An urn has fifteen red balls and nineteen white balls. Three balls are selected at random and the number of red balls are observed.

Find the probability distribution for
Number of Red Balls:
0 =
1 =
2 =
3 =

  • Probability Distribution -

    total amount of balls = 15 red + 19 white = 34 balls

    0 - 0/34 = 0
    1 - 1/34
    2 - 2/34 = 1/17
    3 - 3/34

  • Probability Distribution -

    Prob red = 15/34
    prob white = 19/34

    when picking three:
    prob(0 red) = C(3,0) (19/34)(18/33)(17/32) = 57/352
    prob(1 red) = C(3,1) (15/34)(19/33)(18/32) = 2565/5984
    prob(2red) = C(3,2) (15/34)(14/33)(19/32) = 1998/5984
    prob (3red) = C(3,3)(15/34)(14/33)(13/32) = 455/5984

    notice that the sum of the 4 fractions above is 5984/5984 = 1

  • typo - Probability Distribution -

    the 2nd last prob calculation should be 1995/5984

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