Question

On the lattice of points shown to the right, the lower-left point has coordinates (0, 0) and the upper-right point has coordinates (3, 3). If three points are selected at random, what is the probability that they form a right triangle?

Answer 1

If the range of the possible points that can be chosen is from 0 to 3, then the possible points that can be picked are:
(0, 1), (0, 2), (0, 3)
(1,0), (1, 1), (1, 2), (1, 3)
(2,0), (2, 1), (2, 2), (2, 3)
(3,0), (3, 1), (3, 2)

Only the coordinates (0,3) and (0,3) as the third point will produce a right triangle. The probability equation is:
P = successful outcomes / total outcomes
P = 2 / 10
P = 0.2 or 20%