Let us take the total number of residents as 100.
(1/4) * 100 = 25 residents leave their doors open while 75 keep them closed.
5% of 25 (open doors) = 5 * 25/100 = 1.25 residents will have something stolen while
1% of 75 (closed doors) = 0.75 residents will have something stolen
To find: P(Open doors given that something was stolen), that is
P(Open doors | Something was stolen) = 1.25/(1.25 + 0.75) = 1.25/2 = 0.625.
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