Probability that involves a geometric measure such as length or area is called geometric probability. Suppose that a region A contains a region B.
Suppose now that a point Q in region A is chosen at random. Then, the probability that point Q is in region B is given by the ratio of the area of region B to the area of region A.
P(Qis inB)=Area of regionB/Area of regionAWe can also use angle measures to find geometric probability. The ratio of the area of a circle sector to the area of the entire circle is the same as the ratio of the sector’s central angle to 360. With this in mind, let's consider the given diagram.
We want to find the probability of the pointer not landing on green. This is known as finding the probability of the complement. To do so, we will calculate the probability of the pointer landing on green. Then, we will subtract the obtained result from 1.
P(Not green)
=
1-P(Green)
We can see that the angle measure of the green region is 110^(∘). Knowing that the full circle has a central angle whose measure is 360, we can write the ratio to find the desired probability.
P(Green) = 110/360
As we have already said, let's now subtract P(Green) from 1.
