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How do i determine the probability distribution for this problem?

Consider an experiment in which five fibers, which have lengths one, two , three, four, and five inches, respectively, are tested to see which breaks first. Suppose that the probability that any given fiber will break first is proportional to the length of that fiber. Give the sample space and the probability distribution over the sample space.

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1. X = random variable where fiber of length x will break first. note: total of 1 to 5 = 15 P(X=1) = 1/15 P(X=2) = 2/15 ... P(X = k) = k/15 ... k = 1,2,3,4,5 §
2. = 1/10:2/10:3/10:4/10:5/10 or = 1/10:1/5:3/10:2/5:1/2 or = 10%:20%:30%:40%:50% or simply = 1:2:3:4:5
3. The sample space is the set of all possible outcomes. Let B(x) = the event that the fiber of length x inches breaks first. Then the sample space is: B(1 <= x <=5), x being an integer. Let P(x) = the probability that fiber of length x breaks first. Then, P(1) + P(2) + P(3) + P(4) + P(5) = sigma(1, 5, P(x)) = 1 (since one of the five fibers is sure to break first), And, out of 5 + 4 + 3 + 2 + 1 = 15 trials, P(x) will happen x times. So, P(x) = x/15.