If the item has a 15% chance to drop, then the chance for it not to drop in one run is 85% (or 0.85 for math purposes).

The chance for it not to drop in 2 runs is 0.85*0.85.

The chance for it not to drop in N runs is 0.85^N.

I'm not sure how you're coming up with numbers when he didn't say how many runs he did, but let's say it's 25:

0.85^25 = 0.017197... ~= 1.72% chance of happening.