Re : Probability of any 3 points being on a straight line
A square of length 3 is drawn in the first quadrant with one of the vertexes located at (0,0). A random plotter can mark any integer point located on any edge or an integer point that is located inside the square. If the random plotter is used exactly three times what is the probability that the three points are congruent or form a straight line ?. Assume that the random plotter picks an integer point only once(Each of the three points is distinct). Note an integer point refers to a point (x,y) such that both x and y are integers.
The answer is 0.07857.
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1 solution
There are a total of 16 points where the random plotter can plot points.
Any 3 points can be picked in c(16,3) ways.
There are 10 lines (4 horizontal lines, 4 vertical lines and 2 diagonal lines).
Diagonals :
Each line has 4 points on them. Number of ways to pick 3 distinct points the 4 points forming a line is c(4,3)=4. Total number of ways in which straight lines can result out of these 10 lines are 40..
In addition to these are some more subset of 3 points which when connected will result in forming straight lines. This is shown below
So there are a total of 44 different ways in which 3 randomly selected points can form straight lines. So the probability is 44/c(16,3) = 44/560 = 0.07857