Question 1210173
<pre>

{{{drawing(400,1600/9,-1,8,-1,3,

triangle(0,0,7,0,2.357142857,1.855768722),

green(line(0,0,3.78882,1.28251)),

locate(0,0,B),locate(7,0,C), locate(2.27,2.18,A),
green(locate(3.77,1.6,"D'")),

locate(1.2,1.53,3), locate(3.5,0,7), locate(4.5,1.4,5),

green(locate(2.2,.8,4)), red(line(0,0,2,1),
circle(2,1,.1), locate(2,1.4,P),
line(3.1098313,1.5549156,2.1,1.05),locate(3,2,D))
) 


 )}}}

The figure is drawn to scale. 

BD' is exactly 4 units. So the point P must be chosen inside triangle 
ABD' in order for BD to be < 4, as shown in the red part. 

So we want the probability that point P is chosen inside triangle ABD'. which
will be:  

{{{matrix(1,4,AREA,OF,triangle,"ABD'")/matrix(1,4,AREA,OF,triangle,ABC)}}}

I don't have time right now to find the areas of those two triangles. Maybe
another tutor will do that.  Otherwise, I'll be back tomorrow.

Edwin</pre>