500 seems too small. If someone is 1 in 30,000 on A and 1 in 30,000 on B, then about 1 in a billion will be at least as extreme as them on both A and B. That’s not exactly the number that we’re looking for but it seems like it should give the right order of magnitude (30,000 rather than 500).
And it seems like the answer we’re looking for should be larger than 30,000, since people who are more extreme than them on A+B includes everyone who is more extreme than them on both A and B, plus some people who are more extreme on only either A or B. That would make extreme scores on A+B more common, so we need a larger number than 30,000 to keep it as rare as 1 in a billion.
500 seems too small. If someone is 1 in 30,000 on A and 1 in 30,000 on B, then about 1 in a billion will be at least as extreme as them on both A and B. That’s not exactly the number that we’re looking for but it seems like it should give the right order of magnitude (30,000 rather than 500).
And it seems like the answer we’re looking for should be larger than 30,000, since people who are more extreme than them on A+B includes everyone who is more extreme than them on both A and B, plus some people who are more extreme on only either A or B. That would make extreme scores on A+B more common, so we need a larger number than 30,000 to keep it as rare as 1 in a billion.