Question

A point is chosen at random in a circle of radius 9 cm. The probability
that it is within the distance 2 cm from the centre is
(A)
(A)
ala
4
(B)
81
1
1
(C)
1
m
(D)
81
9​

Answer 1

Step-by-step explanation:

Let S denote the set of points inside the circle with radius r, and let A denote the set of point inside the concentric circle with radius

2

1

r.

Thus, A consists precisely of those points of S which are closer to the center than to its circumference.

Therefore, p=P(A)=

πr

2

π(

2

r

)

2

=

4

1

Answer 2

Answer:

Hence the probability is 4/81.

Given:

A point is chosen at random in a circle of radius 9 cm.

To Find:

Find the probability that it is within the distance 2 cm from the center

Step-by-step explanation:

As it is the case of geometrical probability.

Geometric probability is a tool to deal with the problem of infinite outcomes by measuring the number of outcomes geometrically, in terms of length, area, or volume. In basic probability, we usually encounter problems that are "discrete" (e.g. the outcome of a dice roll)

Geometrical probability = favorable area /  total area

favorable area = area of 2cm radius circle

favorable area = π x 2²

favorable area =4π cm²

Total area = π x 9²

Total area = 81π

So the probability = 4π/81π

=4/81