Statistics (12th Edition)

Published by Pearson
ISBN 10: 0321755936
ISBN 13: 978-0-32175-593-3

Chapter 3 - Probability - Supplementary Exercises 3.154 - 3.199 - Applying the Concepts - Advanced - Page 175: 3.191d

Answer

$P$( All 3 kidneys match receiver) = $0.0000001$% $P$( None of kidneys match receiver) = $99.7003$%.

Work Step by Step

Event A : 1st donor kidney matches receiver. Event B : 2nd donor kidney matches receiver. Event C : 3rd donor kidney matches receiver. $P$( All 3 kidneys match receiver) = $P$(A∩B∩C) $P$(A∩B∩C) = $P$(A)*$P$(B)*$P$(C) $P$(A∩B∩C) = $0.001*0.001*0.001$ $P$(A∩B∩C) = $0.000000001$ $P$(None of 3 kidneys match receiver) = $P$(AUBUC$)^{c}$ $P$(AUBUC$)^{c}$ = 1- $P$(AUBUC) $P$(AUBUC$)^{c}$ = 1- [0.002997] (Please see the picture below) $P$(AUBUC$)^{c}$ = $0.997003 = 99.7003$%
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