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Probability — Maths STD 10 — Question

Gujarat BoardEnglish MediumSTD 10MathsProbability2 Marks
Question
Suppose you drop a die at random on the rectangular region shown in Figure. What is the probability that it will land inside the circle with diameter $1m?$
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Answer

Total area of the given figure (rectangle) = $3\times2=6m^2$
$d =1$
$r=\frac12$
And Area of circle = $\mathrm{πr}^2$= $\mathrm\pi\left(\frac12\right)^2=\frac{\mathrm\pi}4\mathrm m^2$
$Proabibilty\;of\;the\;event=\frac{Number\;of\;favourble\;outcomes}{Total\;number\;of\;possible\;outcomes}$
Hence, $P$(die to land inside the circle) = $\frac{\frac{\mathrm\pi}4}6=\frac{\mathrm\pi}{24}$
Hence the probability of die to land inside the circle is $\frac{\mathrm\pi}{24}$

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