# Probability and Percentiles

• B
I scored in the 88th percentile in a certain personality trait and am trying to figure out the probability of that given that I'm male. I'm trying the likelihood that I would land in the 88th percentile given that I'm male.

Definitions: T = trait, M = males, F = female.
Given:
P(T|M) = 0.3
P(T|F) = 0.6

I'm actually having trouble formulating this in mathematical terms even. I'm not sure where the 0.88 comes into play.

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2021 Award
P(T) doesn't make sense for a continuous trait, and percentiles don't make sense for a binary trait.

So it looks like I'm having to mix binary (male vs female) and continuous (percentile) probabilities and I'm not sure where to starts.

Mentor
2021 Award
The male vs female part is not problematic. It is P(T) that is problematic. Let's say that T is IQ. Then it makes sense to say "I scored in the 88th percentile on IQ", meaning that IQ is a continuous trait and yours is larger than 88% of the population.

But what doesn't make sense is P(IQ). Everybody has an IQ, it isn't a probabilistic thing. What is probabilistic is the score. So you might say P(IQ>100), but you would never say P(IQ)

Oh... So I would formulate it as P(IQ>0.88|M)?

Mentor
0.88 is not a realistic IQ value.
You can ask for P(IQ>yourIQ|M) but that's what you want to get, not what you have given.
Given:
P(T|M) = 0.3
P(T|F) = 0.6
Where does that come from?

@mfb That's completely made up. I'm just trying to get a grasp on how to work with the numbers.

Mentor
Ideally you have the full distribution for males and females, or at least some way to estimate that. Otherwise it will be a lot of guesswork.

Gold Member
Oh... So I would formulate it as P(IQ>0.88|M)?
That is close. You can have the probability of one event given another event. That would be like P( In88Percentile | M ). If you know the fraction of males in the 88th percentile, that is the answer.

Mentor
2021 Award
Oh... So I would formulate it as P(IQ>0.88|M)?
Pretty close. If x is IQ for the 88th percentile then you would write it as P(IQ>x|M).

So, for convenience (I am on a mobile device) let's say X is "a person has a score for T which is in the 88th percentile or higher". Then your question is to find P(X|M). The way to do that is with Bayes theorem:

P(X|M) = P(M|X) P(X)/P(M)

Can you work it out from there?