You explained the subtract 50, but not really the and double.

Revised:

"You ask 100 people the question about illegal activity, and explain they're going to toss the coin and follow the protocol. That gives you 100 "yes" and "no" answers, of which ~50 "yes" answers are yes due to the coin being heads, regardless of whether true yes or false positive, so subtract those yesses out. The remaining yes answers are from the tails results and are not false positives. Because heads/tails is 50% chance, half of your true yesses were on tails, and half on heads. To get back the "hidden" half of yesses you tossed out with the 50 heads results, you double the yesses that came up with tails. That's the data you use to get a final answer."