Probablility Problem

[BillP]

I think that we're making this problem harder than it realy is. If we assume that the answer to Daniel's question is "no", the dots on either line cannot occupy the same point, then the answer is:

for line 1, there is a 50% probability that the intersection falls on a dot
for line 2, there is a 25% probability that the intersection falls on a dot

therefore,

for both to occur, the probablility is 50% x 25% (or mathematically)

0.5 x 0.25 = .125, so there is a 12.5% probability (1 in 8) that both lines will be on dots at the intersection.

Or am I wrong?

(don't think so)

[BillP]

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!