Question

What is the probability that a randomly thrown dart that hits the square board in shaded region the radius of circle is 2 cm the length of square is 4 cm?

Answer 1

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Refer to the attachment !!

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Answer 2

Answer:

Probability of hitting the shaded region = $\frac{3}{14}$

Step-by-step explanation:

i) Radius of the circle (r)=2 cm

$Area\:of \:the \:circle(A_{1})\\=\pi r^{2}\\=\frac{22}{7}\times (2\:cm)^{2}\\=\frac{88 \: cm^{2}}{7}--(1)$

ii) Side of the square = 4 cm

Area of the square $A_{2}$ = a²

= (4 cm)²

= 16 cm² ---(2)

Now ,

Area of the shaded region = Area of the square - Area of the circle

= $A_{2}-A_{1}\\</p><p>= 16-\frac{88}{7}\\=\frac{112-89}{7}\\=\frac{24}{7}--(3)$

Probability of hitting the shaded region = $\frac{Favourable\: Area}{Total\:Area}$

$\implies P(E)=\frac{\frac{24}{7}}{16}\\=\frac{24}{7\times 16 }\\=\frac{3}{14}$

Therefore,

Probability of hitting the shaded region = $\frac{3}{14}$

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