Bayes’s formula Below is Bayes’s formula.
(1)
(2)
(3)
Example : Box P has 2 red balls and 3 blue balls and box Q has 3 red balls and 1 blue ball. A ball is selected as follows:
(i) Select a box (ii) Choose a ball from the selected box such that each ball in the box is equally likely to be chosen. The probabilities of selecting boxes P and Q are (1/3) and (2/3), respectively.Given that a ball selected in the above process is a red ball, the probability that it came from the box P is (GATE CS 2005) (A) 4/19 (B) 5/19 (C) 2/9 (D) 19/30 Solution:
R --> Event that red ball is selected B --> Event that blue ball is selected P --> Event that box P is selected Q --> Event that box Q is selected We need to calculate P(P|R)?P(R|P) = A red ball selected from box P = 2/5 P(P) = 1/3 P(R) = P(P)*P(R|P) + P(Q)*P(R|Q) = (1/3)*(2/5) + (2/3)*(3/4) = 2/15 + 1/2 = 19/30 Putting above values in the Bayes's Formula P(P|R) = (2/5)*(1/3) / (19/30) = 4/19
Exercise A company buys 70% of its computers from company X and 30% from company Y. Company X produces 1 faulty computer per 5 computers and company Y produces 1 faulty computer per 20 computers. A computer is found faulty what is the probability that it was bought from company X?
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