What is wrong with my probability calculation? LEPAINT in july 14

Question : Isn’t P(T /[Li,Ri]) = 1 ? (Li <= T <= Ri). The range [Li,Ri] is given at the end of ith iteration, considering it is part of the input. Doesn’t the question thus resolve to, find expected sum of colour values after i iterations given the following i ranges were randomly coloured (just the colour choosing is random and not the range choosing)?

If choosing the range was random, then the probability of any index being chosen would be 1/(number of ranges that include that index) = 1/(i*(n-i+1)), and there should be no range inputs given, just the number of iterations.

The probability of an index being chosen being 0.5 considering that that index would be chosen or not, means the probability is equal for all of them, implying index 1 and 2 (also considering generally) would have same denominator in their probability computation(for numerator 1), which is not always the case. (n) = (2*(n-1)).

Correct me if I am wrong.

We are not choosing the interval [L,R] but the subsets of [L,R] (not even intervals). So the chance of a block being selected is 0.5 and not 1.!!!

Eg : for [1,4] i can choose {2,4}.

Also, if the range was random then probability of index being chosen is not 1/(number of ranges that include that index) but (number of ranges that include that index)/(all possible ranges)

ok thanks. mistakes on my part.