Answer
$P$(None of kidneys match)= $42.1875$%
Work Step by Step
Event A:1st sibling kidney matches receiver.
Event B:2nd sibling kidney matches receiver.
Event C:3rd sibling kidney matches receiver.
$P$(None of kidneys match)= $P$(Any one kidney matches$)^{c}$ = $P$(A U B U C$)^{c}$
$P$(A U B U C$)^{c}$=1−$P$(A U B U C)
$P$(A U B U C$)^{c}$=$1−0.578125$ (explained below)
$P$(A U B U C$)^{c}$=$0.421875=42.1875$%.
$P$(A U B U C)= $P$(A) + $P$(B) +$P$(C) - $P$(A∩B)- $P$(A∩C)- $P$(B∩C) +$P$(A∩B∩C)
$P$(A U B U C)= $0.25+0.25+0.25 - 3* (0.25*0.25) + (0.25*0.25*0.25)$
$P$(A U B U C)= $0.571825$.
