SOLUTION: In a mixed class, there are 10 girls. If 2 pupils are selected at random, the probability that they are both girls is 0.15 How many boys are in the class?

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Question 673004: In a mixed class, there are 10 girls.
If 2 pupils are selected at random, the probability that they are both girls is 0.15
How many boys are in the class?
Answer by stanbon(75887) About Me  (Show Source):
You can put this solution on YOUR website!
In a mixed class, there are 10 girls.
If 2 pupils are selected at random, the probability that they are both girls is 0.15
How many boys are in the class?
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Let # of boys be "x".
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0.15 = 10C2/(10+x)C2
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0.15 = (45)/[(10+x)(9+x)]/2
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0.15 = 90/[(10+x)(9+x)]
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1/600 = 1/[(10+x)(9+x)]
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(10+x)(9+x) = 600
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x^2+19x+90 = 600
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x^2 + 19x - 510 = 0
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Factor:
(x-15)(x+34) = 0
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Positive solution:
x = 15 (# of boys in the class)
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Cheers,
Stan H.