Let length of side of smaller square = a

Then length of side of bigger square = 1.5a

Area of smaller square = a^{2}

Area of bigger square = (1.5)^{2}a^{2} = 2.25a^{2}.

Probability that dart will land in the interior of the smaller square = (Area of smaller square)/(Area of bigger square) = a^{2}/2.25a^{2} = 1/2.25

∵ Geometrical probability,

P(E) = (measure of specified region part)/(measure of the whole region)