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In the Fig. below, 13, a square dart board is shown. The length of a side of the larger square is 1.5 times the length of a side of the smaller square. If a dart is thrown and lands on the larger square. What is the probability that it will land in the interior of the smaller square?

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Let length of side of smaller square = a

Then length of side of bigger square = 1.5a

Area of smaller square = a2

Area of bigger square = (1.5)2a2 = 2.25a2.

Probability that dart will land in the interior of the smaller square = (Area of smaller square)/(Area of bigger square) = a2/2.25a2 = 1/2.25

∵ Geometrical probability,

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

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