Question

in the fig 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​

Answer 1

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)2a2 = 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)

Answer 2

4/9 is the probability that dart will land in the interior of the smaller square​ if it lands on the larger square

Step-by-step explanation:

length of a side of the larger square is 1.5 times the length of a side of the smaller square

Let say side of smaller square = a

Area of smaller square = a²

Area of interior = a²

Side  of Larger Square = 1.5a

Area of Larger Square = (1.5a)² = 2.25a²

Area of exterior = 2.25a² - a² = 1.25a²

Dart lands in larger square = 2.25a²

Dart land in the interior of the smaller square​ = a²/2.25a²

= 1/2.25

= 4/9

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