Respuesta :
Probability helps us to know the chances of an event occurring. The probability of Linda's dart hitting the circle is 0.7857.
What is Probability?
The probability helps us to know the chances of an event occurring.
[tex]\rm{Probability=\dfrac{Desired\ Outcomes}{Total\ Number\ of\ outcomes\ possible}[/tex]
As it is given that the circle touches the sides of the square. therefore, the length of the side of the square is the diameter of the circle.
Now, in order to calculate the probability that the dart hits a point in the circle we need to calculate the area of the circle and the area of the square.
Area of the circle with a given radius of 9 units,
[tex]\text{Area of the circle} = \pi r^2[/tex]
[tex]\rm = \pi \times (9^2)\\\\= 81\pi\ units^2[/tex]
Area of the square with sides equal to the diameter of the circle,
[tex]\rm \text{Area of square} = side^2[/tex]
[tex]\rm = Diameter ^2\\\\= (2 \times radius)^2\\\\= (2 \times 9)^2\\\\= 18^2\\\\= 324\ units^2[/tex]
Now, the probability that the dart hits a point in the circle can be written as,
[tex]\rm Probability=\dfrac{Desired\ Outcomes}{Total\ Number\ of\ outcomes\ possible}\\\\\\Probability=\dfrac{\text{Area of the circle}}{\text{Area of square}}\\\\\\Probability=\dfrac{81 \pi}{324} = 0.7857[/tex]
Hence, the probability of Linda's dart hitting the circle is 0.7857.
Learn more about Probability:
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