> After running 10 million simulated draws, I got an answer of 0.0323, which matches the real answer very closely.

If you enjoyed reading about how you can approximate complex statistical values using basic programming, I highly recommend Jake Vanderplas "Statistics for Hackers" [0][1].

It converts the sometimes hard to grok statistics terms and formulas into some very simple loops and basic operations.

Can't recommend it enough.

0 - https://speakerdeck.com/pycon2016/jake-vanderplas-statistics...

1 - https://www.youtube.com/watch?v=Iq9DzN6mvYA