Geometric Probability

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

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)

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.

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)

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)