The probability that the dart lands inside the square but not on the circular dartboard is 0.215
The chances of the happening of any event are called the probability.
The dartboard is in the form of a square and the circle is inscribed in it
The area of the dartboard is [tex]a_d=54\ inch^2[/tex]
Since the circle is inscribed on the dashboard so the diameter of the circle will be the length of the square
[tex]a_d=s^2=64[/tex]
[tex]s=\sqrt{64}=8\ inch[/tex]
Thus the diameter of the circle
[tex]d=8\ \ \ r= \dfrac{8}{2} =4 \ inches[/tex]
Now we will calculate the area of the circle
[tex]a_c=\pi r^2[/tex]
[tex]a_c=\ 3.14\times 4^2=50.24\ inch^2[/tex]
The area of the square outside the circle will be the difference of the area of the square and the area of the circle
[tex]64-50.24=13.76\ inch^2[/tex]
Now to find out the probability of the dart hitting outside the circle will be calculated as.
[tex]\rm Probability = \dfrac{Area \ outside \ circle }{Area \ of \ square}[/tex]
[tex]P= \dfrac{13.76}{64} =0.215[/tex]
Thus the probability that the dart lands inside the square but not on the circular dartboard is 0.215
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