The event [(Y1<2*Y2) or (Y1<3*Y2)] is the same as the event (Y1<3*Y3).

This is because the event (Y1<2*Y2) coresponds to points above the line

Y2=(1/2)Y1 in the Y1, Y2 plane, and inside the unit square, and the event

(Y1<3*Y2) coresponds to points above the line Y2=(1/3)Y1 in the Y1, Y2

plane, and inside the unit square. The latter region includes all of the first

region.

Also as Y1 and Y2 are uniformly distributed on the unit square the required

probability corresponds to the area of the the region, which is:

1-(1/6)=5/6.

(the area not in the region is a triangle of base 1 and altitude 1/3).

RonL