11.6 Geom Prob - 11.6 Geometric Probability 11.6 p. 699...

Info iconThis preview shows page 1. Sign up to view the full content.

View Full Document Right Arrow Icon
This is the end of the preview. Sign up to access the rest of the document.

Unformatted text preview: 11.6 Geometric Probability 11.6 p. 699 Probability Probability • Definition - a # from 0 to 1 that represents the chance that an event will occur. will • 0 – no chance • 1 – 100% chance (the event will always 100% occur). occur). • .5 or ½ - 50% chance • Geometric Probability – probability involving lengths or areas. involving Probability & Length Probability A C D B • Let AB be a segment containing CD. • If a pt on AB is chosen at random, then the probability that the point is also on CD is: P( on CD ) length of CD = length of AB P( not on CD ) = 1 − P( on CD ) Example: Example: l 0 1 l 2 l 3 l 4 l 5 l 6 l 7 l l 8 9 l 10 l 11 l 12 l 13 l Y A B C D E F G H 1. Find the probability that a pt. chosen at Find random on YH is on CF. random CF 5 As a percentage? P( on CF ) = = YH 13 about 38% 1. Find the probability that the pt. is on AB. AB 2 As a percentage? = P( on AB ) = YH 13 about 15% Probability & Area Probability J M • Let J be a region that contains a region M. • If a pt. from J is chosen at random, then the If probability that it is also in M is: probability P(in region M ) area of M = area of J Ex: You have a dart board split into Ex You 20 ≅ sectors & a diameter of 2 ft. • What is the probability that a random What dart will land in the sector marked 20? dart area of sector 20 P(20) = area of dart board arc measure 2 area of sector = * πr 360 1 π ft 2 P = 20 π ft 2 πr 2 π (1) 2 18 area of sector = * π (1) 2 360 1 area of sector = π ft 2 20 π ft 2 1 P= 20 Or about 5% Ex: You ride to work on a bus. A bus comes every You 15 min & the ride to work is 31 min. You arrive at the bus stop at 8:24 am. What is the probability that you will be at work at 9:00 am? will • What time do you have to leave the stop by? 8:29 am 5 min l l l l l l l l l 8:24 :26 :28 :30 :32 :34 :36 :37 :39 15 min p (get to work by 9) longest you can wait = max . wait time 5 min 1 = or about 33% 15 min 3 Assignment Assignment ...
View Full Document

This note was uploaded on 02/12/2011 for the course MTG 3212 taught by Professor Jackson during the Spring '11 term at University of Florida.

Ask a homework question - tutors are online