A quality control manager has used algorithm C4.5 to come up with rules that cla

Question

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?

Explanation / Answer

As the word algorithm us used in the question,but the algorithm has not been provided.

So ,I am solving the question with the mathematical approach.

The conditional probablities is calculated based on the Bayes Theorem.The formula for the Bayes theorem is as follows:-

P(B/A) =P(A and B)/P(A)

Here the A and B are two non-independent events.

Now P(Accept)=0.5

P(Reject)=0.5

ALso given in the question that :-

a)5% of good are Rejected= 0.05

b)2% of the bad are Accepted.=0.02

c) Acording to hostorical data 2% of items are bad.=0.02

[I] P(R/G) i.e rejected but are actually good is given by formula

P(G/R)*P(R)/P(G)

Now on putting the values we haev result as:-

(0.05*0.5)/(0.98)

=0.025 or 2.5%

[II] Now we have to calculate the P(A/B) i.e accepted but bad.The formula is given by:-

P(B/A)*P(A)/P(B)

=(0.02*0.5)/0.02

=0.5 or 50%

Hence the conditional probability for the both the parts have been calculated.

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