# Some probability problems for your consideration

As I was preparing this tweet on AMS prizes given at the 2016 Joint Mathematics Meetings…

…I checked the AMS Annual Survey of the Mathematical Sciences to determine that in 2015 roughly 30% of full-time faculty in the mathematical sciences were female. Then, I wrote and did the following math problem:

Question #1: Suppose that 20 people are being chosen for various awards. Assume that for each award, there is a committee that narrows the field of candidates down to a set of 10 finalists who are deserving of the award, and 3 of them are female. Assume that each committee independently chooses the winner from this set of finalists in such a way that each of the finalists is equally likely to win the award. What is the probability that none of the 20 people are women?

That seems really unlikely.

Some people are going to argue that because women have been excluded from the mathematical sciences to a greater degree in our recent history, the population of senior people who have made big contributions to their fields is going to skew even more male than the general population of full-time faculty.  (BTW, not all of the awards above are for senior people who’ve made big contributions.) OK, so let’s consider another problem.

Question #2: Keep everything from Question #1 the same but this time let’s assume that x (in %) of the finalists for each award are men. What would x have to be so that the probability of not having any women chosen is something more likely, like 25%?

Answer: x^20=0.25 means x ≈ .933 ( or 93.3%)

Is it the case that there are so few women deserving of awards in mathematics?

I assert that we don’t suffer from a lack of talented women and people of color in the mathematical sciences. The problem is that we don’t nurture talented women and people of color, don’t recognize their talent, and don’t take enough steps to make sure our award processes are unbiased, fair, and equitable. (There is plenty of evidence that women are just as implicitly biased against women as men are.)

Look at the dramatic change in the representation of people of color in this year’s Oscar nominations, compared to a mere two years ago when #OscarsSoWhite was trending. Did the field suddenly produce a bunch of new Black artists and producers and directors in those two years? No.  So why can’t those of us in the mathematical sciences also try harder to make sure that we make sure award winners are more broadly representative?

Every time a women or person of color looks at a list of winners like this one, they receive messages that they aren’t welcome in the field.

Important caveats:

• These two problems are just food for thought. I’m not implying that the actual awarding of the AMS prizes is anything like what is described above.
• I’m not suggesting that any of the selection committee members were deliberately being racist or sexist.
• I’m not suggesting that any of the winners of the awards were not deserving and should return their prizes.
• Also, my tweet and this post is about the underrepresentation of women, and I also recognize that there is an underrepresentation of African-American, Hispanic/Latinx, and Native American people among the award winners.

It would be interesting to go back in history to look at the demographics of all AMS prize winners.