Probablility Problem

[Kevin Sevcik]

Exhaustively, you can count the number of yeses and divide by the number of nos. In this case, counting nos is easier. Think of your lines there as a grid, with the dots extending as colored lines. You've got 64 total possibilities (8 x 8), and you've got an area there that doesn't have any colored lines which is where you get a no cause there isn't a colored dot there. This area happens to be 24 dots large (6 x 4) ((8-2) x (8-4)).

So. 24/64 odds of it being a no. 40/64 odds of it being a yes. 5/8 = 62.5%

The math with just the percentages goes:

50% of it being blue
+
25% of it being red
-
50%*25% of it being red and blue
=
62.5%

or

100%
-
50%*75% of it not being blue or red
=
62.5%