1. Geometric Probability

2. Let’s consider the following example.
In some cases, we have to calculate the probability of an event involving geometric figures. We call it geometric probability.
Obviously, the event of winning a certain prize is related to the area of the corresponding sector.
Let’s consider the following example.
Now, try to find the probability of winning a pen.
For example: In a game, a player throws a dart at random onto the dartboard as shown. If the dart hits the dartboard, the player will win a prize.
Computer
Pen
Printer
144°
Memo pad

3. Example: Find the probability of winning a pen.
Computer
Let r be the radius of the dartboard, then its area is
Pen
Printer
144°
Area of the blue sector
Memo pad
∴ P(winning a pen)

4. In calculating the geometric probability involving a pie chart,
since
area of sector
angle of the sector = ,
area of circle
round angle
we can simply consider the angle of the sector favourable to a certain event.
Let’s study the following example.

5. The figure shows a lucky wheel
The figure shows a lucky wheel. A player spins the wheel and wins the prize where the pointer stops.
P(winning an MP3 player)

6. Follow-up question
The figure shows a dartboard which is in a shape of a parallelogram. Ann throws a dart at random and the dart hits the dartboard. Find the probability that the dart hits the shaded region. h b
Solution
Let h and b be the height and the base of the parallelogram respectively.
Area of the parallelogram
Area of the shaded region
 The shaded region is a triangle.
∴ P(hitting the shaded region)