Exercise 1 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 AD is chosen at random, and want to find the probability that the point X lies on BD.

The probability that the point X is on BD is the ratio of the length of BD to the length of AD. P(X is onBD)=BD/AD Looking at the given number line, we can see that BD= 5 and AD= 10.

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

P(X is onBD)=BD/AD

SubstituteII

BD= 5, AD= 10

P(X is onBD)=5/10

ReduceFrac

a/b=.a /5./.b /5.

P(X is onBD)=1/2

WriteDec

Write as a decimal

P(X is onBD)=0.5

WritePercent

Convert to percent

P(X is onBD)=50 %

The probability that the point X lies on BD is equal to 12, which can be also written as 0.5 or 50 %.