Questions : In the given figure, points A, B, C and D are the centres of four circles that each have a radius of length one unit. If a point is selected at random from the interior of square ABCD. What is the probability that the point will be choosen from the shaded region?
Doubt by Vanshika
Solution :
Radius of circle (r) = 1 unit
Side of square (a) = 2× Radius of circle
a=2r
a=2×1
a=2 units
Side of square (a) = 2× Radius of circle
a=2r
a=2×1
a=2 units
Total possible area
= Area of square
= a2
=(2)
=4 sq. units
Area of favorable region
= area of square - area of 4 sectors having θ=90°
= area of square - area of 4 sectors having θ=90°
=a2-4×(θ/360°)×πr2
=(2)2-4×(90°/360°)×π(1)2
= 4-4×(1/4)π
= 4-π
= 4-4×(1/4)π
= 4-π
P(E) = (No. of favorable outcomes) / (Total No. of possible outcomes)
P(The point will be choosen from the shaded region)
= (4-π)/4
= (4-3.14)/4
= 0.86/4
= 0.215
= (4-π)/4
= (4-3.14)/4
= 0.86/4
= 0.215
Similar Question :
In the given figure, points A, B, C and D are the centres of four circles that each have a radius of length one unit. If a point is selected at random from the interior of square ABCD. What is the probability that the point will be choosen from the shaded region?
In the given figure, points A, B, C and D are the centres of four circles that each have a radius of length one unit. If a point is selected at random from the interior of square ABCD. What is the probability that the point will be choosen from the shaded region?
a) 1-(π/4)
b) 1-(π/2)
c) 1-(π/6)
d) 2-(π/4)