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Unread 08-08-2005, 13:54
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Re: Probablility Problem

OK, I think I was wrong. I too, misread the problem. As I see it now, you are looking for the probability of ANY dot being at the intersection, not both lines having a dot there. This changes everything.

It is easy to see that there is a 50% chance of finding a dot on the first line and a 25% chance for the second, but the probability of either or is additive (with a twist), not multiplicative.

To start, there is a 50% probability that the first line will intersect on a dot and a 25% chance for the second so, if we add these together, we get a 75% chance of hitting a dot ... BUT WAIT ..., 50% of the time, when the second line is on a dot, the first line will ALREADY BE ON A DOT so we have to subtract these from the probability. So the final equation becomes:

50% + 25% - (50% x 25%) -- or mathematically

0.50 + 0.25 - (0.50 x 0.25) = .625 == or 62.5% probability of EITHER line intersecting on a dot.

Geeez, I hate making mistakes!
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