Exercise 28 Page 914

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

The probability that the point X is on RT is the ratio of the length of RT to the length of QT. P(X is onRT)=RT/QT Looking at the given number line, we can see that RT= 8 and QT= 14.

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

P(X is onRT)=RT/QT

SubstituteII

RT= 8, QT= 14

P(X is onRT)=8/14

ReduceFrac

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

P(X is onRT)=4/7

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Convert to percent

UseCalc

Use a calculator

P(X is onRT)=0.571429...

RoundDec

Round to 3 decimal place(s)

P(X is onRT)≈0.571

WritePercent

Convert to percent

P(X is onRT)≈ 57.1 %

The probability that the point X lies on RT is equal to 47 or about 57.1 %.