Question

in the adjoining figure a die is thrown it lands in the interior of circle what is the probability that the dive in land in the shaded region




pls frnds answer my quest​

Answer 1

diameter of the given circle =6cm
hence r=3cm

area of a circle = πr²
=3.14×9
=28.26cm²

area of the rectangle inscribed in the circle
= A(ΔADC) + A(ΔABC)
=½( AC×OD) + (AC×OB)
=½(6×3)+(6×3)
=½×18+18
=½×36
=18cm²

area of shaded region = A(circle) -A(rectangle)
=28.26-18
=10.26cm²

the probability that the die will in land in the shaded region
= area of shaded region/ area of a circle
=10.26/28.26
=1026/2826
=513/1413
=171/471
=57/157

hence the probability is
$\frac{57}{157}$

hope this helps :-)