Exercise 8 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 HK.

The probability that the point X is on HK is the ratio of the length of HK to the length of FK. P(X is onHK)=HK/FK Looking at the given number line, we can see that HK= 20 and FK= 36.

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

P(X is onHK)=HK/FK

SubstituteII

HK= 20, FK= 36

P(X is onHK)=20/36

ReduceFrac

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

P(X is onHK)=5/9

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Write as a decimal

UseCalc

Use a calculator

P(X is onHK)=0.5

RoundDec

Round to 2 decimal place(s)

P(X is onHK)≈ 0.55

WritePercent

Convert to percent

P(X is onHK)≈55 %

The probability that the point X lies on HK is equal to 59, which can be also written as 0.55 or about 55 %.