Statistic Question - I am trying to solve this problem but I dont know how! Could someone help me? Thank you!

Question

Of a finance company`s loans, 1% are defaulted (not completely repaid). The company routinely runs credit checks on all loan applicants. It finds that 30% of defaulted loans went to poor risks, 40% to fair risks and 30% to good risks. Of the nondefaulted loans, 10% went to poor risks, 40% to fair risks, and 50% to good risks. Use Bayes’ formula to calculate the probability that a poor-risk loan will be defaulted.

 

Answer 1

D: event that  loan is defaulted

ND:  event that loan is non-defaulted

P(D)=0.1, P(ND)=0.99

PR:event  that loan is poor risk,

FR: event that loan is fair risk

GR: event that loan is good risk

P(PR/D) =0.3, P(PR/ND) =0.1

P(PR∩D) =(PR/D)*P(D )= .3 * .01 = 0.003, P(PR∩ND) = P(PR/ND) * P(ND) = .1 * .99= 0.099 [Baeyes theorem]

P(PR) =  P(PR∩D) + P(PR∩ND) = 0.102

probability that a poor-risk loan will be defaulted = P(D/PR) = P(PR∩D) / P(PR) = 0.003/0.102 =0.029 = 2.9% [Baye's theorem]