Question

The popular bank has estimated, from previous experiences, that the probability of an upr student failing to pay a student loan is 0.31. It has also estimated that 35% of loans not paid on time have been made to finance tuition and 65% of loans paid on time have been made to finance tuition.
a) Calculate the probability that a loan made to finance tuition will not be paid on time.
b) Calculate the probability that if the loan made for purposes other than tuition payments will be paid on time.

Answer 1

given :

P(not paid on time) = 0.31

P(tuition | not paid on time) = 0.35

P(tuition | paid on time) = 0.65

a.

P(tuition) = P(tuition | not paid on time)*P(not paid on time) + P(tuition | paid on time)*P(paid on time)

= 0.35*0.31 + 0.65*(1-0.31)

= 0.557

P(not paid on time | tuition) = P(tuition | not paid on time)*P(not paid on time) / P(tuition)

= 0.35*0.31 / 0.557

= 0.1948

b.

P(not tuition) = 1 - P(tuition)

= 1 - 0.557

= 0.443

P(paid on time | not tuition) = P(not tuition | paid on time)*P(paid on time) / P(not tuition)

= (1- P(tuition | paid on time))*P(paid on time) / 0.443

= (1 - 0.65)*(1-0.31)/0.443

= 0.5451

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