Exercise 6 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 FH.

The probability that the point X is on FH is the ratio of the length of FH to the length of FK. P(X is onFH)=FH/FK Looking at the given number line, we can see that FH= 16 and FK= 36.

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

P(X is onFH)=FH/FK

SubstituteII

FH= 16, FK= 36

P(X is onFH)=16/36

ReduceFrac

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

P(X is onFH)=4/9

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Write as a decimal

UseCalc

Use a calculator

P(X is onFH)=0.4

RoundDec

Round to 2 decimal place(s)

P(X is onFH)≈ 0.44

WritePercent

Convert to percent

P(X is onFH)≈44 %

The probability that the point X lies on FH is equal to 49, which can be also written as 0.44 or about 44 %.