# Math

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A bucket contains blue balls and yellow balls. the probability of removing two blue balls without replacement is 2/5 and he probability of removing three blue balls without replacement is 1/5. Why must there be two more blue balls then yellow balls? How many red balls were in the bucket. show that b=y+2

• Math -

b/(b+y) * (b-1)/(b+y-1) = 2/5
b/(b+y) * (b-1)/(b+y-1) * (b-2)(b+y-2) = 1/5 = 1/2 * 2/5

so,

(b-2)/(b+y-2) = 1/2
2(b-2) = b+y-2
2b-4 = b+y-2
b = y+2

no idea about any red balls, but

(y+2)/(2y+2) * (y+1)/(2y+1) = 2/5

(y+2)/2(2y+1) = 2/5
5y+10 = 8y+4
3y = 6
y=2
so, b=4

4/6*3/5 = 2/5
2/5*2/4 = 1/5

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