Exercise 9 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 FG.

The probability that the point X is on FG is the ratio of the length of FG to the length of FK. P(X is onFG)=FG/FK Looking at the given number line, we can see that FG= 4 and FK= 36.

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

P(X is onFG)=FG/FK

SubstituteII

FG= 4, FK= 36

P(X is onFG)=4/36

ReduceFrac

a/b=.a /4./.b /4.

P(X is onFG)=1/9

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Write as a decimal

UseCalc

Use a calculator

P(X is onFG)=0.1

RoundDec

Round to 2 decimal place(s)

P(X is onFG)≈ 0.11

WritePercent

Convert to percent

P(X is onFG)≈11 %

The probability that the point X lies on FG is equal to 19, which can be also written as 0.11 or about 11 %.