Exercise 1 Page 937

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 AE is chosen at random, and want to find the probability that the point X lies on AC.

The probability that the point X is on AC is the ratio of the length of AC to the length of AE. P(X is onAC)=AC/AE Looking at the given number line, we can see that AC= 18 and AE= 40.

We can substitute these values in the above formula to find the probability that the point lies on AC.

P(X is onAC)=AC/AE

SubstituteII

AC= 18, AE= 40

P(X is onAC)=18/40

ReduceFrac

a/b=.a /2./.b /2.

P(X is onAC)=9/20

▼

Convert to percent

ExpandFrac

a/b=a * 5/b * 5

P(X is onAC)=45/100

WriteDec

Write as a decimal

P(X is onAC)=0.45

WritePercent

Convert to percent

P(X is onAC)=45 %

The probability that the point X lies on AC is equal to 920, which can be also written as 45 %.