06.03.2013 Views

Artificial Intelligence and Soft Computing: Behavioral ... - Arteimi.info

Artificial Intelligence and Soft Computing: Behavioral ... - Arteimi.info

Artificial Intelligence and Soft Computing: Behavioral ... - Arteimi.info

SHOW MORE
SHOW LESS

Create successful ePaper yourself

Turn your PDF publications into a flip-book with our unique Google optimized e-Paper software.

P (E / H) . P (H)<br />

So, P (H / E) = (9.1)<br />

P (E)<br />

which is known as Bayes’ theorem.<br />

Example 9.2: Consider the following problem to illustrate the concept of<br />

joint probability of mutually independent events <strong>and</strong> dependent events.<br />

A box contains 10 screws, out of which 3 are defective. Two screws are<br />

drawn at r<strong>and</strong>om. Find the probability that none of the two screws are<br />

defective using a) sampling with replacement <strong>and</strong> b) sampling without<br />

replacement.<br />

Let A: First drawn screw is non-defective.<br />

a) Sampling with replacement<br />

P(A) = 7/10<br />

P(B) = 7/10<br />

B: Second drawn screw is non-defective.<br />

P(A ∩ B) = P(A).P(B) = 0.49<br />

b) Sampling without replacement<br />

P(A) = 7/10<br />

P(B/A) = 6 / 9 =2 / 3<br />

P (A ∩ B) = P(A).P (B/A) = 14 / 30 = 0.47<br />

Now, for reasoning under uncertainty, let us concentrate on the well-known<br />

Bayes’ theorem. With reference to our medical diagnosis problem,<br />

P(D / S) = P (S / D) . P(D) / P(S) (9.2)

Hooray! Your file is uploaded and ready to be published.

Saved successfully!

Ooh no, something went wrong!