A quality control manager has used algorithm C45 to come up

A quality control manager has used algorithm C4.5 to come up with rules that classify items based on several input factors. The output has two classes -- Accept and Reject. Test results with the rule set indicate that 5% of the good items are classified as Reject and 2% of the bad items classified as Accept. Historical data suggests that two percent of the items are bad. Based on this information, what is the conditional probability that: (i) An item classified as Reject is actually good? (ii) An item classified as Accept is actually bad?

Solution

P(Bad Items) =0.02

P(Good Items) = 1-0.02=0.98

P(Rejection of good items) = 0.05 * 0.98 = 0.049

P(Acceptance of bad items) = 0.02 * .02 = 0.0004

(i)

P(Good Item/Reject Item) = P(Rejection of good item)/P(Rejection)

= 0.049/(0.049 + (1-0.0004))

=0.0467 Answer

(ii)

P(Bad Item/Accept Item) = P(Acceptance of bad item)/P(Acceptance)

= 0.0004/(0.0004 + (1-0.049))

=0.0004 Answer