+130511 We can construct a square with its bottom left edge at (0,0), its top left edge at (0,2), its top right edge at (2,2) and its bottom right edge at (2,0)....all the points within this square will have x, y coordinates between 0 and 2
So......the total area of this square = 4 units^2
And the probability that a point in this square lies exactly 1 unit from the origin will be the collection of points in the quarter circle contained in this square with a radius of 1 unit......and the area of this circle = (1/4)pi (1)^2 = pi/4
So....the probability that any chosen point lies less than 1 unit form the origin will be a little less than :
[ pi/ 4] / 4 = pi / 16 ≈ .196
Here's a picture of the situation :
+130511 We can construct a square with its bottom left edge at (0,0), its top left edge at (0,2), its top right edge at (2,2) and its bottom right edge at (2,0)....all the points within this square will have x, y coordinates between 0 and 2
So......the total area of this square = 4 units^2
And the probability that a point in this square lies exactly 1 unit from the origin will be the collection of points in the quarter circle contained in this square with a radius of 1 unit......and the area of this circle = (1/4)pi (1)^2 = pi/4
So....the probability that any chosen point lies less than 1 unit form the origin will be a little less than :
[ pi/ 4] / 4 = pi / 16 ≈ .196
Here's a picture of the situation :
