At a mortgage company, 60% of calls are answered by an attendant. The remaining 40% of callers leave their phone numbers. Of the
se 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.
1 answer:
Answer:
24/35, about 69%
Step-by-step explanation:
The data given can be put into a 2-way table (attached). It shows that 0.48 of all calls were answered and resulted in a mortgage application. Altogether, 0.70 of all calls resulted in a mortgage application. Thus the conditional probability of interest is ...
p(spoke to attendant | applied for a mortgage) = p(spoke & applied)/p(applied)
= 0.48/0.70 = 24/35 ≈ 69%
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