Question 836154
a box contains 7 identical red balls, 4 identical white balls and 9 identical black balls. 3 balls are taken out from the box one after another without replacement. what the probability that 
i)2 of them are red and one is black
# of ways to succeed:: 7C2*9 = 21*9 = 189
# of random triples: 20C3 = 1140
P(2red AND 1black) = 189/1140
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ii)all three balls have different colour
# of ways to succeed:: 7*4*9 = 252
# of random triples: 1140
P(diff colors) = 252/1140
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iii) at least one ball is white::
P(at least one white) 1 - P(no white)
P(no white) = (11/16)^3 = 0.325
P(at least one white = 1-0.325 = 0.675
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iv)all three have same colour
# of ways to succeed: 9C3+7C3+4C3 = 123
P(all same color) = 123/1140
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Cheers,
Stan H.
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