We can use geometric models to solve certain types of probability problems. In geometric probability, points on a segment or in a region of a plane represent outcomes. The geometric probability of an event is a ratio that involves geometric measures such as length or area. Consider the given diagram.
We are told that a point on AK is chosen at random, and want to find the probability that the point satisfies the inequality x ≤ 1.
Note that the inequality defines the segment AB. The probability that the point is on AB is the ratio of the length of AB to the length of AK.
P(The point is onAB)=AB/AK
Looking at the given number line, we see that AK= 10 and AB= 1.
We can substitute these values in the above formula to find the probability that the point lies on AB. This is the same as finding the probability that the point satisfies the given inequality.
P(The point is onAB)=AB/AK ↓ P(The point is onAB)=1/10
