Q. 295.0( 1 Vote )

# Coloured balls are distributed in four boxes as shown in the following table:A box is selected at random and then a ball is randomly drawn from the selected box. The colour of the ball is black, what is the probability that ball drawn is from the box III.

Given:

Box I has 3 Black, 4 White, 5 Red, 6 Blue balls

Box II has 2 Black, 2 White, 2 Red, 2 Blue balls

Box III has 1 Black, 2 White, 3 Red, 1 Blue balls

Box IV has 4 Black, 3 White, 1 Red, 5 Blue balls

Let us assume U1, U2, U3, U4 and A be the events as follows:

U1 = choosing Box I

U2 = choosing Box II

U3 = choosing Box III

U4 = choosing Box IV

A = choosing Black ball from box

We know that each urn is most likely to choose. So, probability of choosing a urn will be same for every Urn.

The Probability of choosing balls from each box differs from box to box and the probabilities are as follows:

P(A|U1) = P(Choosing black ball from Box I)

P(A|U2) = P(Choosing black ball from Box II)

P(A|U3) = P(Choosing black ball from Box III)

P(A|U3) = P(Choosing black ball from Box III)

Now we find

P(U3|A) = P(The black ball is from BallIII)

Using Baye’s theorem:

The required probability is .

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