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11.6 Geom Prob

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

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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 ...
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