The probability if there was 0 correlation is of course 0.5. So using IQ as a criteria beats random selection by 16.67% (as Taleb also found). This is a little more than 6%, but that is a detail. More importantly, this example is a theoretical use case where using IQ testing is not so useful. To look at something a little more realistic, let’s say a company wants to avoid people with a performance more than 2 standard deviations below the mean. (Perhaps such employees have a risk of causing large harm, which could for instance be an issue in the military.) And we again compare admitting people at random vs only taking applicants with above average IQ.
If the company admits people at random, we get this proportion of people with a performance more than 2 SD below the mean: