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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
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"=(1.5x)^2`
`=2.25 x^2 cm^2`
`"Area of smaller square"=x^2 cm^2`
`"We know that Probability" = "Number of favourable event"/"Total number of event"`
Hence probability that the dart will land in the interior of the smaller square is equal to `= x^2/(2.25 x^2)=4/9`
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