Exercise 7 Page 902

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

The probability that the point X is on GJ is the ratio of the length of GJ to the length of FK. P(X is onGJ)=GJ/FK Looking at the given number line, we can see that GJ= 26 and FK= 36.

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

P(X is onGJ)=GJ/FK

SubstituteII

GJ= 26, FK= 36

P(X is onGJ)=26/36

ReduceFrac

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

P(X is onGJ)=13/18

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Write as a decimal

UseCalc

Use a calculator

P(X is onGJ)=0.72

RoundDec

Round to 2 decimal place(s)

P(X is onGJ)≈ 0.72

WritePercent

Convert to percent

P(X is onGJ)≈72 %

The probability that the point X lies on GJ is equal to 1318, which can be also written as 0.72 or about 72 %.