Question

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 =
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

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
the 2nd last prob calculation should be 1995/5984

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