Answer: The probability that the lengths of the three segments are the side lengths of a triangle is 0.25.
Step-by-step explanation:
Consider the event "S" as "The three segments are the sides of a triangle." Remember that the probability of an event occurring is calculated according to:
By dividing the stick into three segments, the possible cases that can be obtained writing each case in parenteses and the length of each piece as a number are:
(1, 1, 10), (1, 2, 9), (1, 3, 8), (1, 4, 7), (1, 5, 6), (2, 2, 8), (2 , 3, 7), (2, 4, 6), (2, 5, 5), (3, 3, 6), (3, 4, 5), (4, 4, 4).
which corresponds to a total of 12 total cases.
The necessary condition so that a triangle can be formed is that the sum of its two minor sides is greater than the greater side, therefore the favorable cases would be:
(2, 5, 5), (3, 4, 5), (4, 4, 4)
which corresponds to a total of 3 favorable cases. Using the probability formula we obtain: