himanshuhpr wrote:
A certain computer program randomly generates equation of line is form of y=mx+b.If point p is a point on a line generated by this prog, what is probability that line does not pass through ABCD.
a)3/4 b)3/5 c)1/2 d)2/5 e)1/4
I think the question seems to be fine and solution that Karishma provided is excellent.
If one can notice in original picture posted, cooridnates of point C ,D and P are such that angle DPC is 90. (This can be verified using coordinates or slopes)
Thus, for any line of the form y=mx+b, passing through point P. There is a 90' region from which it can not pass, else it will go inside the square ABCD. Outside of this 90 it can pass wherever it wants. it will be ok.
There is overall 180' region, starting from x-asis and going in anticlock wise, where this line can be drawn. (considering only above x-axis - as once you rotate line enough to go below x-axis, the other end of line would be above x-axis)
Thus probability = Total favourable area/Total area = 1/2
Now, coming to how it is 90' and 180'. We can consider this solution only in first quadrant or in first & fourth quadrant both. However when we consider both quadrants, since it will provide a mirror image across x-axis.
total area, which is not desired, formed by line = 90*2 and total area possible for line = 180*2 = 360
still you get same ans 1/2.