Base rates
Why rare things stay rare, even after a warning sign.
In your head, jot if needed · a calculator helps on some problems why?
Opens at level 28.
Lesson and untimed practice
Read the full lesson and try each skill without a clock. About 3 minutes to read.
skills · practice stats
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What a flag means not tried yet
worked example
Out of 10,000 parts, 5% are defective. An inspection machine flags 90% of defective parts and wrongly flags 2% of good ones. What percent of flagged parts are actually defective? Round to the nearest percent.
Answer: 70%
- 500 defective → 450 flagged (90%). 9,500 good → 190 flagged (2%).
- 450 of the 640 flags are real: 450 ÷ 640 ≈ 70.3%, about 70%.
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At least once not tried yet
worked example
Each product launch has a 10% chance of a serious bug. Over 18 independent launches, what is the chance of at least one serious bug? Round to the nearest percent.
Answer: 85%
- The chance of none in all 18 is 0.9¹⁸ ≈ 0.15.
- So at least one: 1 − 0.15 = 0.85, about 85%.
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Regression to the mean not tried yet
worked example
The restaurant with the worst inspection score in town is inspected again the next month. Assuming nothing changed in the kitchen, what should you expect from its second score?
- an even more extreme result
- exactly average results
- no change
- some improvement, since extreme results tend to drift back toward average
Answer: some improvement, since extreme results tend to drift back toward average
- An extreme result is usually partly real and partly chance. The chance part tends not to repeat, so the next result usually lands closer to average.
- That's regression to the mean: expect some improvement even when nothing changes.
rest ladder
- 1 day
- 3 days
- 7 days
- 14 days
- 30 days
- 60 days
- mastered · every 90 days