The average number of iterations performed by binary search depends on the probability of each element being searched. The average case is different for successful searches and unsuccessful searches. It will be assumed that each element is equally likely to be searched for successful searches. For unsuccessful searches, it will be assumed that the intervals between and outside elements are equally likely to be searched. The average case for successful searches is the number of iterations required to search every element exactly once, divided by formula_2, the number of elements. The average case for unsuccessful searches is the number of iterations required to search an element within every interval exactly once, divided by the formula_112 intervals.