Question

there are 2 semicircles in the figure.O is the centre of the larger semicircle.put a dot in this figure without looking.
(a) if the radius of the smaller
semicircle is r. what is the
radius of the larger semi
circle?
(b) what is the probability that
the dot would be within the
smaller semicircle?
(c) what is the probability that
the dot would be outside
the semicircle?
I want the answer. its very urgent. so that can u pls help me ​

Answer 1

Answer:

Let the radius of the smaller semi-circle be r.

Thus area of smaller semi-circle =

2

πr

2

Now, area of larger semi-circle =

2

π(2r)

2

=4×

2

πr

2

=4 (Area of smaller semi-circle)

P(Point is inside the semi-circle)=

Areaoflargersemi−circle

Areaofsmallersemi−circle

=

2

4πr

2

2

πr

2

=

4

1

Thus, probability that the point is inside the smaller semi-circle is

4

1