Some motivation for the non-math folks out here - twitter shows an ad on your timeline. Assume the chances of twitter getting a callback on that ad is uniform (

Some motivation for the non-math folks out here - twitter shows an ad on your timeline. Assume the chances of twitter getting a callback on that ad is uniform ( very unlikely, but play along ). That means roughly 50% of folks will ignore the ad or dismiss the ad, the rest will actually engage with the ad impression. Lets say twitter makes a dollar per engagement. How many ads need to be shown to make the first dollar ? Two dollars ? How about five, ten, hundred, or a million ? That's what this problem gets at.And in case you are curious about the solution to all that money - ---- scala> def uniform = util.Random.nextDouble def sumsTo(n:Int) = { var (times, sum) = (0.0d,0.0d); while(sum < n) { sum += uniform; times += 1.0d; }; times } def meanSumsTo(n:Int) = (1 to 1000000).map(_=>sumsTo(n)).sum/1000000.0d List(1,2,5,10,100,500,1000).map(x=> (x,meanSumsTo(x)) scala> res1: List[(Int, Double)] = List((1,2.718594), (2,4.672438), (5,10.665755), (10,20.668308), (100,200.65537), (500,1000.669558), (1000,2000.669246)) ---- So you need to show 3 ads to make a buck, 5 ads to make $2 etc.