The probabilityis usuallywrittenas , or. Sometimesthis is expressedas “a 50-50chance”
becausethe probabilityof successand of failureare both.
GeometricProbability
The valuesof and that determinea probabilitycan be lengthsand areas.
Example 3
Seanneedsto drill a hole in a wall that is feet wide and feet high.Thereis a 2-foot-by-3-footrectan-
gularmirroron the otherside of the wall so that Seancan’tsee the mirror. If Seandrills at a randomlocation
on the wall, whatis the probabilitythat he will hit the mirror?
The area of the wall is squarefeet. This is.The area of the mirroris squarefeet. This is.The probabilityis.Example 4
Ella repairsan electricpowerline that runs from Actonto DaytonthroughBartonand Canton.The distances
in milesbetweenthesetownsare as follows.
- Bartonto Canton= 8 miles.
- Actonto Canton= 12 miles.
- Cantonto Dayton= 2 miles.
If a breakin the powerline happens,whatis the probabilitythat the breakis betweenBartonand Dayton?
Approximately.= the distancefrom Actonto Dayton miles.= the distancefrom Bartonto Dayton miles.LessonSummary
Probabilityis a way to measurehow likelyor unlikelyan eventis. In this sectionwe saw how to use lengths
and areasas modelsfor probabilityquestions.The basicprobabilityideasare the sameas in non-geometry
applications,with probabilitydefinedas: