A cloth of $10$ meter is to be randomly distributed among $3$ brothers. Find the probability that no one can get more than $4$ meter. (Cloth may be distributed as $3.5$m, $3.5$m and $3$m. Or $3.2$m, $3.8$m and $3$m)
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Please clarify the probability distribution. – Mårten W Feb 06 '13 at 16:14
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is the length of the cloth continuous or some sorta discrete? – bryan.blackbee Feb 06 '13 at 16:15
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Normalize the length to 1. Pick two points a, and b with these constraints: $a<1, b<1, a+b<1$. Assuming uniform distribution, on cartesian coordinates, this corresponds to a triangle. Now, add the constraint that you want $\max(a,b,1-(a+b))<x.$ For $x<\frac12$, this area will be $\frac{x^2}2$. Therefore the probability is $x^2$. Plugging your units will give $p=0.16$. Should be straigtforward to convert this to integration since what we done is simple area calculation.
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