At a mortgage company, 60% of calls are answered by an attendant. The remaining 40% of callers leave their phone numbers. Of these 40%, 75% receive a return phone call the same day. The remaining 25% receive a return call the next day. Of those who initially spoke to an attendant, 80% will apply for a mortgage. Of those who received a return call the same day, 60% will apply. Of those who received a return call the next day, 40% will apply. Calculate the probability that a person initially spoke to an attendant, given that he or she applied for a mortgage.

A First Course in Probability (10th Edition)
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ISBN:9780134753119
Author:Sheldon Ross
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Chapter1: Combinatorial Analysis
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At a mortgage company, 60% of calls are answered by an attendant. The
remaining 40% of callers leave their phone numbers. Of these 40%, 75%
receive a return phone call the same day. The remaining 25% receive a
return call the next day.
Of those who initially spoke to an attendant, 80% will apply for a mortgage.
Of those who received a return call the same day, 60% will apply. Of those
who received a return call the next day, 40% will apply.
Calculate the probability that a person initially spoke to an attendant, given
that he or she applied for a mortgage.

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