Suppose three of the labeled points are chosen at random. What is the probability that the chosen points are collinear?
We are told in the question that three of the four points are chosen at random. This means that there are four different combinations of points that could be chosen. We could choose 𝐹, 𝐺, and 𝐻. We could also choose 𝐹, 𝐺, and 𝐾. Thirdly, we could choose 𝐹, 𝐻, and 𝐾. And finally, we could have chosen the points 𝐺, 𝐻, and 𝐾.
We need to work out the probability that the chosen points are collinear. This means that they must lie in the same straight line. The only set of three points that are collinear are 𝐹, 𝐺, and 𝐻, as all three of these lie on the same straight line.
We know that the probability of an event occurring is the number of successful outcomes over or divided by the number of possible outcomes. In this case, there is one successful outcome when we choose the points 𝐹, 𝐺, and 𝐻 and four possible outcomes.
We can, therefore, conclude that the probability that the three chosen points are collinear is one out of four or one-quarter. This could also be written as a decimal, 0.25, or a percentage, 25 percent.