Advertisement Remove all ads

In Below Fig., Points A, B, C and D Are the Centers 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 Chosen from the Shaded Region? - Mathematics

In below Fig., points A, B, C and D are the centers 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 chosen from the shaded region?

Advertisement Remove all ads

Solution

Radius of circle = 1cm

Length of side of square = 1 + 1 = 2cm

Area of square = 2 × 2 =` 4cm^2`

Area of shaded region = area of square – 4 × area of quadrant

= 4 – 4 `(1/4) pi(1)^2`

= (4 − 𝜋)` cm^2`

Probability that the point will be chosen from the shaded region =`"Area of shaded regfion"/"Area of square ABCD"`= `(4−pi)/4` = 1 −`(pi/4)`

Since geometrical probability,

P(E) =`"Measure of specified part of region"/"Measure of the whole region"`

  Is there an error in this question or solution?
Advertisement Remove all ads

APPEARS IN

RD Sharma Class 10 Maths
Chapter 16 Probability
Exercise 16.2 | Q 4 | Page 33
Advertisement Remove all ads
Advertisement Remove all ads
Share
Notifications

View all notifications


      Forgot password?
View in app×