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Consider the 20 points of a 4×5 grid. You randomly choose two points from the 20 points. What is the probability that the two points belong to a horizontal or vertical line?

 Sep 2, 2021
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Assuming we can't choose the same 2 points:

 

We have 3 points in the same column, or 4 points in the same row, that are valid points to choose, that would result in the dots making a row or column.

 

Out of the 19 other points you can choose after the first one, there are 7 that match the initial condition.

 

Therefore, the probability is 7/19.

 

Sorry I don't have a better explanation, but I'm not really a fan of using latex to make graphics.
... You know what, I'll do it anyways

 

Here's an example. X is the point we choose, C are the dots that make a vertical line, and R are the ones that make a horizontal line.

 

\(\begin{bmatrix}X & R & R & R & R \\ C &&&&\\ C &&&&\\ C &&&&\end{bmatrix}\)

 Sep 2, 2021

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