An auditing model correctly predicted bankruptcy of 90% of...

An auditing model correctly predicted bankruptcy of 90% of firms that in fact did fail and correctly predicted non-bankruptcy of 80% of firms that did not fail. Besides, the historical data shows that 30% of firms for which the model made its prediction did fail in the last year. a/ Find the probability that the model will predict bankruptcy for a firm. b/ Find the probability that a firm will go bankrupt, given that the model has predicted it will do so.

Transcript

00:01 Hi, i'm david and i'm here to help you answer your question.

00:03 Now let me pick up your question here.

00:07 Now in this question i'm going to summarize this one by the three diagrams.

00:12 So we have the 30 % of the firm will be predicted that will fail in the last year.

00:22 So i will say this one will be failed and then not fail will be the c complement.

00:27 30 % of them will be predicted to fail in the last year so it will be 0 .3 for this and the common will be 0 .7 and now we have the model that will correctly predict the bankruptcy of 90 % so this one will be bankruptcy not bankruptcy same thing here bankruptcy and then not bankruptcy now for those companies fail in the last year the model will correctly predict bankruptcy of the 90 % so it will be correctly will be 0 .9 for the bankruptcy and then the complement will be the 0 .1 for those that not fail the model will predict that 90 % correctly so it will be 0 .a for the correctly and the common here will be 0 .2 so that will be the 3 diagram here now for the part i .m.

01:27 The question the question asking us to find the probability that the model will predict bankruptcy for firm so probability of the bank of c and here notice that you go to the bank of c we need to go first this brand and then we go this branch here or we go to the not fail and then we go to the bank of c so therefore it just equal to the product of the 0 .3 times when the 0 .9 plus 0 .7 times with the 0 .2.

02:01 And we do the calculation, get equal to the 0 .41 for the a.

02:11 Now for the b, we will have the probability that the firm will not go bankruptcy.

02:17 So probability that not bankruptcy, given that the model has predicted, it will saw, given that the predicted.

02:27 Predicted so for the probability that the firm will not go bankruptcy...

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