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jmc

counting and probability intermediate

Problem

Two different numbers are selected simultaneously and at random from the set . What is the probability that the positive difference between the two numbers is or greater? Express your answer as a common fraction.
Solution
The only time the two numbers selected will not have a positive difference which is 2 or greater is when the two numbers are consecutive. There are 6 pairs of consecutive numbers in the set , and there are pairs of numbers total. So, the probability that the pair of numbers chosen is not consecutive is .
Final answer
\frac{5}{7}