Another error: you have P(ban) = (0.3 · 0.005) + (0.001 · 0.995) but it should be P(ban) = (0.3 · 0.005) + (0.01 · 0.995) (0.001 would be 0.1% false positive rate, not 1% as you stipulate). This results in P(problem|ban) = 14.85% rather than 13.1%.
(Also, I am actually not sure how you got 13.1%. With the aforementioned error, the result would be 60.1%…)
You are correct I added an extra 0, writing (0.3 · 0.005) + (0.001 · 0.995) when I meant (0.3 · 0.005) + (0.01 · 0.995). That’s a transcription error, thank you for catching it.
I’m not sure how you’re getting 14.85% or 60.1% though? I just checked, and I think those numbers do wind up at ~13.1%, not 14.85%.
Another error: you have
P(ban) = (0.3 · 0.005) + (0.001 · 0.995)
but it should beP(ban) = (0.3 · 0.005) + (0.01 · 0.995)
(0.001 would be 0.1% false positive rate, not 1% as you stipulate).This results in P(problem|ban) = 14.85% rather than 13.1%.(
Also, I am actually not sure how you got 13.1%.With the aforementioned error, the result would be 60.1%…)You are correct I added an extra 0, writing
(0.3 · 0.005) + (0.001 · 0.995)
when I meant(0.3 · 0.005) + (0.01 · 0.995).
That’s a transcription error, thank you for catching it.I’m not sure how you’re getting 14.85% or 60.1% though? I just checked, and I think those numbers do wind up at ~13.1%, not 14.85%.
Yep, my mistake. I’m not sure either! Math is hard, it seems…
EDIT: That is, I’m not sure how I got 14.85%—that was, like, I pressed the wrong calculator keys, or something. But 60.1% is like this:
(0.3 · 0.005) / ((0.3 · 0.005) + (0.01 · 0.995)) = ~0.60120 = 60.12%