Geometry Probability

Questions on probability may also involve geometry and geometrical shapes.

Example:

ABCD is a square. M is the midpoint of BC and N is the midpoint of CD. A point is selected at random in the square. Calculate the probability that it lies in the triangle MCN.

Solution:

Let 2x be the length of the square.

Area of square = 2x × 2x = 4x²

Example:

The figure shows a circle with centre O and radius 8 cm. Ð BOD = 72˚. The radius of the smaller circle is 4 cm. A point is selected at random inside the larger circle BCDE.

Calculate the probability that the point lies
a) inside the sector BODC.
b) inside the smaller circle
c) neither in the sector BODC nor in the smaller circle.

Solution:

a)

Area of sector BODC = × area of the large circle

Probability that the point lies in sector BODC =

b)

Area of smaller circle = × area of the large circle

Probability that the point lies in the smaller circle =

c) Probability that the point does not lie in sector BODC or the smaller circle

=

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