The Bolt Factory

This is my solution to a problem called The Bolt Factory. The problem statement follows

In a bolt factory, machines A, B, and C manufacture 25%, 35%, and 40% of the total output, and have defective rates of 5%, 4%, and 2%, respectively. A bolt is chosen at random and is found to be defective. What are the probabilities that it was manufactured by each of the three machines?

This is a simple Bayes’ theorem problem. Let P(A), P(B), and P(C) denote the probability of the bolt being produced by A, B, and C, respectively. Let also P(D) indicate the probability of the bolt being defective. I will only calculate the probability of the defective bolt being manufactured by A and B with the theorem as the defective bolt must have been produced by one of the machines and, therefore,

P(A|D) + P(B|D) +  P(C|D) = 1

what makes calculating P(C|D) with the theorem unnecessary.

P(D) will be calculated beforehand to speed things up. By the total probability theorem, it is known that

P(D) = P(D|A)P(A) + P(D|B)P(B) + P(D|C)P(C)
     = (.05)(.25) + (.04)(.35) + (.02)(.4)
     = .0345

P(A|D) = P(D|A)P(A) / P(D) = (.05)(.25) / (.0345) ~= 0.3623
P(B|D) = P(D|B)P(B) / P(D) = (.04)(.35) / (.0345) ~= 0.4058
P(C|D) ~= 1 - 0.3623 - 0.4058 = 0.2319

Why Forbid Object Cloning

These are the reasons why I chose to forbid object cloning:

  • cloning is a risky extralinguistic object creation mechanism;
  • cloning demands adherence to thinly documented conventions;
  • cloning conflicts with the proper use of final fields;
  • cloning throws unnecessary checked exceptions;
  • cloning requires casts.

How cloning conflicts with final fields

Say Foo has a final Bar field. Bar is mutable but the field is final. When cloning Foo, you would need to fix the field by doing:

// ...
Foo clone = (Foo) super.clone();
clone.bar = (Bar) bar.clone(); // Impossible !
return clone;
// ...

which is impossible.

Hello, World!

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My name is Bernardo Sulzbach and I am writing this because I can.

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