In an essay competition the odds against competitors A, B, C, and D are 2:1, 3:1, 4:1, and 5:1 respectively. Find the probability that one of them wins the competition.
The answer is 127/150 but I cannot find that answer either online or by myself. I know that the odds against them translates to probabilities of 2/3, 3/4, 4/5, and 5/6 respectively but for starters those numbers do not add up to one. Subtracting one from those numbers and adding them sums to 0.95, which is helpful and intuitive but not the answer. I tried finding the probabilities of each one winning and the others losing and adding those but that was not correct either. Any help is greatly appreciated because this kind of stuff drives me crazy. Here is the URL of the question (first one of the practice GRE test):
GRE Practice Test - Problem Solving GRE Practice Test 5