Question 1163207
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The lengths of the two shorter sticks together must be greater than the length of the longest stick.<br>
(a) The three sticks are now 2, 3, and 4 feet long.  2+3=5 is greater than 4; yes, you get a triangle.<br>
(b) The three sticks are now 1, 3, and 5 feet long.  1+3=4 is less than 5; no, you don't get a triangle.<br>
(c) Either with logical analysis, or with formal algebra, you can determine that the 6-foot stick can be cut at anywhere from 1.5 feet to 4.5 feet from one end to have the three sticks form a triangle (because the difference between 1.5 feet and 4.5 feet is 3 feet -- the length of the other stick.)<br>
The range of where the cut can be made is then 4.5-1.5=3 feet; and the full length of the second stick is 6 feet.  So the probability that the second stick gets cut in a way that makes it possible to form a triangle is 3/6 = 1/2.<br>