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The midpoint of line segment JK is M. What is the probability that a randomly selected point on line segment JK is closer to M than to J or to K?
Draw the picture: a line segment with end points J and K
Put the midpt M in the center of JK
Put "A" half-way between J and M
Put "B" half-way between M and K
All the points between A and B are
closer to M than to J or K.
But segment AB is 1/2 of JK
Probability of a random point being a point of AB is 1/2