## Thursday, October 24, 2013

### surf's up

What if I tried to teach you some math?  I know, a word problem...  the most dreaded thing in all of mathematics.  Let's make it about probability, one of the most misunderstood and difficult things for folks to master.  Wanna try?

This is a problem offered to our students this week in the monthly Florida Math league contest.  Lots of schools across the state participate.  Not many of our kids got it, but surely you are smarter that a high school student, right??

The Surfboard Store sells Special Surfboards that
are so carefully made that only 1 in 1 thousand
is bad. The store tests all Special Surfboards
using a test that is 99% accurate.  If you buy
a Special Surfboard that tests bad, what is the
probability that it really is bad?

Think about it a while and put your answer in the comments here or at the forum where this is posted. (or you can message me if you're shy) I will try to explain the answer tomorrow.

P(board tests bad) = (999/1000)(.01) + (1/1000)(.99) = 0.01098

The .01 in the first part is the probability that a test which is 99% accurate incorrectly says a good board is bad.
The .99 in the second part is the probability that a bad board is correctly identified.

P(board tests bad and is bad) = [(1/1000)(.99)]/0.01098 = 0.09016 or 9.016%

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2. Thanks so much Neil and Kyle for your thoughts. I wonder if part of the problem with questions like these is decifering the language. Of course that is the difficulty in a lot of problems isn't it?? You can check out my thoughts and solution here. http://debcostello.blogspot.com/2013/10/surfs-up-solution.html

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4. Neil,
When you are looking at conditional probabilities like this you have to take into account all of the options. It helps if you draw a tree diagram so that you can see all of the possibilities. There are four possible outcomes in this scenario.
Board Good and Tests good