## Monday, December 29, 2008

### BRAINTENANCE QUIZ 12/29/08

Dear Friends:

Today's quiz is certain to make you think. But then, that's the objective, isn't it?

A bucket contains 50 painted golf balls. 30 are painted blue, and the balance are painted red. Assume that the balls have been well shuffled around, and that you are blindfolded (in a non-hostile situation, and not for the purposes of doing anything that your sainted parents wouldn't approve of). Here are three questions:

1. What is the percentage likelihood (probability) that a ball that you choose will be red?

2. What is the probability that, if the first ball was red and eliminated from the game, that the next ball that you selected would be blue?

3. What is the probability that, if the first ball's color was not identified and eliminated from the game, that the next ball that you selected would blue?

Good luck!

Faithfully,

Douglas Castle
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The solution to yesterday's problem follows:

The sum of all of the integers from 1 to 1,000, inclusive, will be 500,500. If you tried to obtain this answer by plugging numbers into your calculator, it would have taken you (if you're an average sort of person, but focused only on doing this repetitive operation) in excess of one hour, with a high probability of making at least one error.

The formula for adding any series of consecutive numbers from 1 to n (where n is the highest number) is simply: n(n+1)/2. In this particular problem, the computation (which would have saved you the better part of an hour) would have been 1,000(1001)/2.  