I’m honored to be quoted. :) And this was really fun. I wish I’d had students who went out and applied it like that! You are impressive, Jen! :)

]]>So I *think* it should be (1/8) x (1/8) x (1/14) + (1/8) x (1/8) x (1/14)

= 1/896 + 1/896 = 2/896 = 1/448

Let’s test it by figuring it another way. (Because that’s the way I roll.)

Let’s call T the actual top bracket winner.

Let’s call B the actual bottom bracket winner.

Let’s call U the actual undead winner.

The probability of guessing that T wins the top bracket is 1/8.

The probability of guessing that B wins the bottom bracket is 1/8.

So then, yes, there are only 14 books left to choose from, so now the probability of guessing that U is the undead winner is 1/14.

So P(Guessing T wins top bracket AND B wins bottom bracket AND U wins undead poll) = 1/8 x 1/8 x 1/14 = 1/896

But suppose you actually guess that U wins its bracket, and whichever of T or B it knocked out, you guess to be the undead winner. You would still have the right three books in the finals, you just didn’t guess their path to get there correctly, but that doesn’t matter.

Let’s break it into two cases and add up the two probabilities.

Suppose you guess that T is the undead winner. Since you’re starting there, that has a 1/16 probability.

Now, the probability that U is in the top bracket is 1/2.

Then the probability that you guess U wins the top bracket is 1/7, since we already know that T is not the winner.

The probability that you guess B wins the bottom bracket is 1/8.

So, P(guessing T is the undead winner AND U is in the top bracket AND U wins top bracket AND B wins bottom bracket) = 1/16 x 1/2 x 1/7 x 1/8 = 1/1792

Now suppose you guess that B is the undead winner. Probability is 1/16.

The probability that U is in the bottom bracket is 1/2.

The probability that you guess U wins the bottom bracket is 1/7.

The probability that you guess T wins the top bracket is 1/8.

So, P(guessing B is the undead winner AND U is in the bottom bracket and U wins bottom bracket and T wins top bracket) = 1/16 x 1/2 x 1/7 x 1/8 = 1/1792.

Adding up those two probabilities gives us

P(guessing U to win its bracket and the winner it knocked out to win undead poll) = 1/1792 + 1/1792 = 1/896

So, yes, we end up with the same numbers! We add up those two probabilities for our final probability, which *does* match what we got above, *with Jen’s correction*!

P(guessing the right three books in the finals regardless of how they get there) = 1/896 + 1/896 = 1/448

Isn’t this fun?! (It’s at this point that all the students in my Statistics 101 classes would totally HATE me!)

(Aren’t you glad I switched careers and became a librarian?)

]]>At some point, I’m going to collates all your awesome comments for a follow-up point, but phew this week is full…

]]>