SOLUTION: 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 probab

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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
ii)all three balls have different colour
iii) at least one ball is white
iv)all three have same colour
Answer by stanbon(75887) About Me  (Show Source):
You can put this solution on YOUR website!
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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