A man has some marbles which is red, green or blue. He picks one marble out of the bag, looks at its colour keeps it. Then he picks another marble and checks its colour.
The probablity that he picks out two red marbles is 12%
The probablity that he picks out two green marbles is 5%
The probablity that he picks out two blue marbles is 15%
What is the smallest number of blue marbles in the bag?
Two.
The probability that he picks out two blue marbles may be 15%, but it is possible to pick the only two blue marbles out of the bag.
November 28th, 2009 at 11:25 pm
Two.
The probability that he picks out two blue marbles may be 15%, but it is possible to pick the only two blue marbles out of the bag.
References :
November 28th, 2009 at 11:40 pm
ans: 10 blue, 9 red, 6 green , total 25
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working :
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let B be blue marbles and T be total marbles,
then P[2 blue] = [B/T]*[(B-1)/(T-1)]
= B(B-1) / T(T-1)
LCM of 12, 5 ,15 & 100 is 600.
put 600 as the denominator T(T-1)
so T = 25
B(B-1)/600 = 15% = 90/600
so B = 10
others fit in neatly
check :
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P[2 blue] = [10/25][9/24] = 90/600 = 15%
P[2 red] = [9/25][8/24] = 72/600 = 12%
P[2 green] = [6/25][5/24] = 30/600 = 5%
References :