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Question

Coloured balls are distributed in four boxes as shown in the following table:
Box Colour
Black White Red Blue
I
II
III
IV
3
2
1
4
4
2
2
3
5
2
3
1
6
2
1
5
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.

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Solution

Let A, E1, E2, E3 and E4 denote the events that the ball is black, box I selected, box II selected, box III is selected and box IV is selected, respectively.

PE1=14 PE2=14 PE3=14 PE4=14Now, PA/E1=318PA/E2=28PA/E3=17PA/E4=413 Using Bayes' theorem, we getRequired probability = PE3/A=PE1PA/E1PE1PA/E1+ PE2PA/E2 =14×1714×318+14×28+14×17+14×413 =1716+14+17+413=156947


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