## Tuesday, August 29, 2017

### Teach 180: A Banged Up Knee (Day 2)

My second day of classes went really well and then the unexpected happened.  Two unexpected things, actually.  First, we did a simulation in Probability and Statistics.  The scenario: an airline company needs to select 8 pilots at random from a group of 15 male and 10 female pilots.  The results obtained by the airline were 5 females and 3 males.  But wait, shouldn't we have more males than females?  That is what one might think based on the ratio of the original group.  Is it likely to get these results (5 females and 3 males) by chance alone?  We used playing cards to simulate the results and the dotplot here shows our collective results.

Note the one dot at 8.  That happened in 1 out of 65 simulated trials.  But is it really that likely?  Is there a 1.5% chance of this happening?  We conducted a simulation in Fathom and never got 8 in our 2000 simulated trials.  Next, we calculated the theoretical probability and found it to be about 4 out of 100,000.  It's not that getting 8 is impossible, but it is extremely, extremely, extremely, extremely, extremely unlikely.

So, what was the second unexpected thing?  If you read the title to this blog, you guessed it.  Two minutes after the school day ended, I slipped in some water that someone had spilled in the hall.  I came crashing down on my right knee in the process.  At this moment, my knee hurts to bend it and it is being iced.  A special thanks to my advisees in the hallway, Annie and Elliot, for making sure I was ok.