Question
Coloured balls are distributed in four boxes as shown in the following table:
|
Box |
Colour |
|||
|
Black |
White |
Red |
Blue |
|
|
I |
3 |
4 |
5 |
6 |
|
II |
2 |
2 |
2 |
2 |
|
III |
1 |
2 |
3 |
1 |
|
IV |
4 |
3 |
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?
Solution
Let A, E1, E2, E3 and E4 be the events as defined below:
A : a black ball is selected E1 : box I is selected
E2 : box II is selected E3 : box II is selected
E4 : box IV is selected
Since the boxes are chosen at random.
Also, 
P(box III is selected, given that the drawn ball is black) = P(E3 | A).
