Question

A home mortgage loan officer for a large mortgage bank has kept records on the customers...

  1. A home mortgage loan officer for a large mortgage bank has kept records on the customers who visited her office in the past 5 years. Her records indicate that half of her visitors have been women and 20% of the women who visited her ultimately took a mortgage loan from the bank. On the other hand, only 15% of the men who visited her office ultimately took a mortgage loan from the bank.
  1. If a customer visited the loan officer and decided to take a home mortgage loan from her bank, what is the probability that the customer was a man? Show the necessary work.  
  2. If a customer visited the loan officer and decided not to take a home mortgage loan from the bank, what is the probability that the customer was a woman? Show the necessary work.    
  3. Please calculate the probability that a customer who visited the home mortgage officer will take a home mortgage loan from the bank clearly showing how you arrived at your answer.           
Math   Statistics-And-Probability   
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Answer #1

a)P(decided to take loan)=P(women and decided to take loan)+P(men and decided to take loan)=0.5*0.2+0.5*0.15=0.175

therefore P(men given decided to take loan)=P(men and decided to take loan)/P(decided to take loan)=0.5*0.15/0.175=0.428571

b)

P(women given not decided to take loan)==P(women and not decided to take loan)/P(not decided to take loan)

=0.5*(1-0.20)/(1-0.175)=0.484848

c)P(decided to take loan)=P(women and decided to take loan)+P(men and decided to take loan)=0.5*0.2+0.5*0.15=0.175

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