If someone has a success rate of 90%, they fail twice as often as someone who has a success rate of 95% (10 times per 100 vs 5 times per 100) If someone has a success rate of 98% they fail twice as often as someone who has a success rate of 99% (2 times per 100 vs 1). Why is this the same?

Question

If someone has a success rate of 90%, they fail twice as often as someone who has a success rate of 95% (10 times per 100 vs 5 times per 100) If someone has a success rate of 98% they fail twice as often as someone who has a success rate of 99% (2 times per 100 vs 1). Why is this the same?

In: Mathematics

Answer 1

Alright so after additional reflection on the given feedback, I’ve realized the specific relationship I was looking for (and I have no idea why this didn’t occur to me initially) is that in both instances, the difference in failure rate is doubling.

If you’re successful 90% of the time, you fail 10%. If you’re successful 95% of the time, you fail 5%.

If you’re successful 99% of the time, you fail 1%. If you’re successful 98% of the time, you fail 2%.

Similarly, if you have a success rate of 60% you fail twice as often as someone who has a success rate of 80%.

The relationship between the differences of 99%-98%, 95%-90%, and 80%-60% is that the rate of failure between the two is doubled. For some reason my brain didn’t intuitively pick up on that.