SOLUTION: 888.One stick is three times as long as another. You break the longer stick at a random point. Now you have three sticks. What is the probability that they form a triangle?

Question 1163206: 888.One stick is three times as long as another. You break the longer stick at a random point. Now you have three sticks. What is the probability that they form a triangle?
Answer by greenestamps(13198) (Show Source): You can put this solution on YOUR website!

Let the lengths of the two sticks be x and 3x. Call the short stick stick A.

The longer stick is broken into two sticks. Call them the left stick and the right stick.

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.

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.

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.

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.

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