Question 1163206
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Let the lengths of the two sticks be x and 3x.  Call the short stick stick A.<br>
The longer stick is broken into two sticks.  Call them the left stick and the right stick.<br>
If the length of the left stick is less than x, then the length of the right stick is greater than 2x, and the lengths of A and the left stick together will be less than the length of the right stick, and no triangle can be formed.<br>
If the length of the left stick is greater than 2x, then the length of the right stick is less than x, and the lengths of A and the right stick together will be less than the length of the left stick, and no triangle can be formed.<br>
So, in order to be able to form a triangle, the length of the left stick must be between x and 2x, a range of x.<br>
And since the length of the original second stick was 3x, the probability that the three sticks form a triangle is x/3x = 1/3.<br>