11c) Let’s say someone ID’s one of two colors with 80% success. If the color exists in 10% of the population, the other color is misidentified in 18% of total IDs. So how sure can we be it's the minority based on an identification? Around 31%.
This asks something like - was the car you saw blue or green? - and sets a condition that there is a 20% chance of identification error (I say blue when it was green). Further, if green is seen in only 10% of the total of all cars added together, then we know 2% of green answers are incorrect; green is incorrectly called blue 18% of the time.
If you write it out, it looks like this:
- Blue car is correct answer - 72%
- Blue car is incorrect answer - 2%
- Green car is correct answer - 8%
- Green car is incorrect answer - 18%
So if you add up the percentages and take the proportion, you get the odds of each answer being correct:
- Probability blue is correct: 72/74 = 97.3%
- Probability blue is incorrect: 2/74 = 2.7%
- Probability green is correct: 8/26 = 30.8%
- Probability green is incorrect: 18/26 = 69.2%
In other words, if someone says they saw the less frequently seen car, it only takes a small identification error rate before the answer becomes more than 50% likely to be incorrect.
