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A random box contains tags marked 1; 2; …; n. Two tags are chosen at random with replacement.
Find the probability that the numbers on the tags will be consecutive integers.
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The space of events is (n x n)-matrix, whose (i,j)-cell contains the pair of indexes (i,j).
The order does matter and the entire matrix is the space, incliding the diagonal.
Each separate cell / (pair) has the probability .
The favorable outcomes asre the cells located closest to the diagonal (so called one upper-diagonal and one lover diagonal).
The number of favorable outcomes is (n-1) + (n-1) = 2*(n-1).
Therefore, the probability to get two consecutive number randomply is P = . ANSWER
Solved.