In the given figure, a square dart board is shown.

Question:

In the given figure, 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?

Solution:

Given: 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

To find: Probability that it will land in the interior of the smaller square

Let the length of smaller square is x cm

Therefore the length of side of bigger square will be 1.5x cm

Area of bigger square $=(1.5 x)^{2}$

$=2.25 x^{2} \mathrm{~cm}^{2}$

Arca of smaller square $=x^{2} \mathrm{~cm}^{2}$

We know that Probability $=\frac{\text { Number of favourable event }}{\text { Total number of event }}$

Hence probability that the dart will land in the interior of the smaller square is equal to $=\frac{x^{2}}{2.25 x^{2}}=\frac{4}{9}$.