Probability of Making a Triangle.
Given a 4 by 4 grid of dots,
if you choose three distinct points randomly, what is the probability (as a decimal) that connecting the three points will yield a non-degenerate triangle? Round to the nearest thousandth.
Notes: A degenerate triangle is a line. Assume that you are forced to choose three distinct points (as if selecting without replacement).
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1 solution
Use the complement of the probability of getting a non-degenerate triangle. That is, find the probability of getting a degenerate triangle (a line) and subtract that from 1: P(Triangle) = 1 - P(Line) There are 10 lines with four dots (4 vertical, 4 horizontal, and 2 long diagonals), and 4 lines with three dots (medium diagonals), so P(Lines) = 1 6 P 3 1 0 ( 4 P 3 ) + 4 ( 3 P 3 ) Which equals 3 3 6 0 2 4 0 + 2 4 = 3 3 6 0 2 6 4 roughly equaling .921