Math Club: Conditional Probability

February 7, 2017

It's a good day when stuffed animals come to math group. Today they taught my kids about conditional probability.

Examples:

[Without replacement]

Gail: Okay, so you close your eyes, thrust a hand into the bag, and select an animal at random. Ooops, you got Louissss the Python. He strangles you. But you can rest in the knowledge that you've removed a lethal animal from the bag, so the rest of your classmates now have an improved chance of survival.

Gail: Ah, you got Teddy. He's an "annoying" animal, so he tap-dances on your head while belting "Danny Boy" off key. [She demonstrates.] Now, with an annoying animal out of the mix, [next kid], what are your now-reduced chances of not dying horribly when you take the plunge?

[Next exercise, with replacement]

Okay, this time we ARE replacing, but we'll draw ten times and compare our results to the theoretical model. [Visiting Grandma], would you like a turn? Awww, you got Ursa Major. She's friendly and gives you a hug.
Kid: Even the lethal stuffed animals know to leave a grandma alone!

Gail: ... so our model was close, but it predicted one person would be maimed by polio and that didn't happen...

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When I did this two years ago, several kids cheated. This time, though, the kids were really good and didn't cheat! It was nice that I had so much less skew this time between my predicted model and actual results!