We will start by solving the inequality. Then, we will find the probability that a point chosen at random from AK satisfies the inequality.
Solving the Inequality
Let's solve 2x≤ 8.
2x≤8 ⇔ x≤4
We found that x is less than or equal to 4.
Finding the Probability
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≤ 4.
Note that the inequality defines the segment AE. The probability that the point is on AE is the ratio of the length of AE to the length of AK.
P(The point is onAE)=AE/AK
Looking at the given number line, we see that AK= 10 and AE= 4.
We can substitute these values in the above formula to find the probability that the point lies on AE. This is the same as finding the probability that the point satisfies the given inequality.
