OK, I'm falling in love with the latest in bad TV, "Next". For those who don't know, this is where one person (say, "Brittany") would date up to five guys ("Josh, Jereme, Cory, Alex, and T-Lo"). At any time in the date, Brittany can holler "Next!" and the date would end; the next guy/loser would then emerge. Also, she can choose to stop at any time (not unlike "Press Your Luck") and choose that guy for a second date.
The nerd in me identifies this as a classic Markov chain. A Markov chain is a statstical model for a process where the state changes in discrete steps - like when Brittany yells, "Next!". A matrix is derived listing out the state transition probabilities; one can then multiply the matrices together to see the probabilities of being in a certain state in 3, 4, or more steps.
For instance, if P(Kellen Winslow gets hurt doing one wheelie) = .5, the Markov chain would be:
Healthy Injured
Healthy .5 .5
Injured 0 1
(For now, we assume that Kellen will never move from Injured to Healthy...... a pretty good assumption, no?)
We could then multiply the matrix 5 times to see the probability that Kellen is hurt after his 5th wheelie.
What a fascinating Markov chain we can draw for Next. Making up probabilities...
Josh Jereme Cory Alex T-Lo Winner
Josh 0 .9 0 0 0 .1
Jereme 0 0 .8 0 0 .2
Cory 0 0 0 .6 0 .4
Alex 0 0 0 0 .5 .5
T-Lo 0 0 0 0 0 1
Winner 0 0 0 0 0 0
what's the chances that Brittany will pick somebody after 3 dates? What's the disadvantage of going first?
Answering these questions are an exercise for the reader. Wow, I wish my grad class had questions like this instead of the generic ones we had. The ways math can be made more interesting.....
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