You are mistaken. If probability of each of the 5 men being colorblind is independent (so eg. they're not related etc), then there's a 41% chance that at least one of them is (1 - 0.9⁵).

(There's a 33% chance that exactly one of them is: 0.1 × 0.9⁴ × ⁵C₁).

Thanks. It's been too long since I've studied statistics. Might be time to watch some khan academy.

Oh, I see. Assuming probability that a man is not colorblind is 0.9, then you found the probability of none of them being colorblind and subtracted that amount from 1 to find the other side.

For anyone reading this that was bothered by my use of a specific gender, it's because colorblindness occurrence is significantly higher in men than women.

That's not soo much lower, though.

I think a Poison distribution would be more appropriate here, so the probability of 1 man in 5 being colorblind, assuming 10% of the population on average is colorblind, is:

    e^-0.5*sum((i)->(0.5^i/factorial(i)), 1:5) = ~39%

> Poison distribution

Why? This is basic statistics (% of population).

I don't believe so - it's n instances of a bi-valued random variable, IID. It's exactly the case the binomial distribution covers.

Exactly. You have five chances at an event, and an event probability per chance, which is exactly what the binomial distribution is for.

The Poisson distribution is what you use when the effective number of chances is "large". The Poisson distribution is effectively a special case of the binomial distribution, where the number of chances is infinity, the probability per chance is infinitesimal, and the product of the two is the expected number of events.

I also have red/green colorblindness, but it's not as if color coding would have an 8-12% failure rate. Typical red/green color-indistinguishability mostly applies to dark reds and green, though, whereas the reds/greens used in UI tend to be quite bright and vivid.

People who can't distinguish vivid reds/greens are much rarer. (If 10% of men couldn't separate red from green at the stoplight, we'd have noticed a long time ago.)

I agree we should include everyone, of course, which is why there should also be patterns, shapes, and sound to assist, I'm just saying color coding is not some collossal mistake.

(Also, your math is off if you're assuming a 10% base rate. To have at least a 50% chance of 1 person in a group of men being color blind, you need 7 men. 1-(.9^7)= 52%.)

>Yet the world insists on using red/green as bad/good indicators. Drives me nuts.

Well, it has to use something, and other people would be colorblind in other colors, plus some will be blind too.

In this case, one would expect there'd be some OS-wide color utility to alter colors to the ones the user can discern.

Yes, but these other ones are far more rare. Also there are shades that make it so much assessable for people. Almost every day I will ask someone what color something is because of poor selection. Chances are you have a color blind person in you office, just run visualizations by them really quick.

> Chances are you have a color blind person in you office, just run visualizations by them really quick.

This is a great check, but I also recommend trying things just in greyscale as a simple test and installing something like Color Oracle [0]. Also, most of the problems can be solved by looking for an already existing solution, like swapping your heatmap colour scales for viridis [1].

The most important thing is recognising that these kinds of issues exist and pro-actively looking for good current solutions (the same applies for things like trying to ensure your site works well with screen readers).

I'd love to hear of more tools or other things that can help if people have suggestions!

0 http://colororacle.org/

1 https://cran.r-project.org/web/packages/viridis/vignettes/in...