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N.P.Bali; P.N.Gupta; Dr C.P.Gandhi Laxmi Publications PDF

16

Bayes� Theorem and its Applications

16.1. INTRODUCTION

Let there be two or more urns, each containing some white balls and red balls. Suppose an urn is chosen at random and a ball is drawn from that chosen urn. By using addition theorem and multiplication theorem, we can find out the probability of drawing a white ball

(or a red ball) from the urn chosen.

But in case, we are given that the ball drawn is white and we are interested in finding the probability of the event that the ball was drawn from the first urn or the second urn, then the situation is not same as in the previous case. Now the probability of urn drawn will depend upon the colour of the ball drawn.

To tackle this type of problems, Bayes� theorem is used. This theorem was enunciated by British mathematician Thomos Bayes in 1763.

16.2. BAYES� THEOREM

(P.T.U., M.B.A. DEC., 2009, 2012)

Statement. Let E1, E2, ........, En be n mutually exclusive and exhaustive events, with non-zero probabilities, of a random experiment. If A be any arbitrary event of the sample space of the above experiment which occurs with E1 or E2 or ...... or En and P(A) > 0, then

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