Question

3. In the figure there are two semicircles. O is the centre of the larger semicircle,
A fine dot is placed into the figure without looking into it.
a) If the radius of the smaller semicircle is taken as 'r', what will
be the radius of the larger semicircle ?
b) What is the probability of being the dot inside the smaller semicircle ?
c) What is the probability of being the dot outside the smaller semicircle ?​

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

.