The probability that a student is not a swimmer is 1 5  Then the probability that
out of five students, four are swimmers is
(A)
4
5
4
4
1
C
5
5
⎛
⎞
⎜
⎟
⎝
⎠
(B)
44
1
5
5
⎛
⎞
⎜
⎟
⎝
⎠
(C)
4
5
1
1
4
C 5
⎛5
⎞
⎜
⎟
⎝
⎠
(D) None of these
Miscellaneous Examples
Example 33 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 © NCERT
not to be republished
PROBABILITY      579
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 III is selected
E4 : box IV is selected
Since the boxes are chosen at random,
Therefore
P(E1) = P(E2) = P(E3) = P(E4) = 1
4
Also
P(A|E1) = 3
18 , P(A|E2) = 2
8 , P(A|E3) = 1
7  and  P(A|E4) = 4
13
P(box III is selected, given that the drawn ball is black) = P(E3|A)