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 sector of a circle to the area of the entire circle is the same as the ratio of the central angle of the sector to 360. With this in mind, let's consider the given diagram.
We want to find the probability of the pointer landing on neither red nor yellow. This is known as finding the probability of the complement. To do so, we will calculate the probability of the pointer landing on red and the probability of the pointer landing on yellow. Then, we will subtract the obtained results from 1.
P(Not red and not yellow)
=
1-(P(Red)+ P(Yellow))
We can see that the angle measures of the red and yellow regions are 92^(∘) and 44^(∘), respectively. We can use these values to create ratios out of 360.
P(Red) = 92/360 P(Yellow) = 44/360
As we have already said, let's now subtract these two results from 1.
