NCERT Solutions
Class 12 Maths
Probability

Ex.13.4 Q.12
Two numbers are selected at random (without replacement) from the first six positive integers.
Let X denotes the larger of the two numbers obtained. Find E(X).
The two positive integers can be selected from the first six positive integers without replacement in 6 × 5 = 30 ways
X represents the larger of the two numbers obtained.
Therefore, X can take the value of 2, 3, 4, 5, or 6.
For X = 2, the possible observations are (1, 2) and (2, 1).
So, P(X = 2)
For X = 3, the possible observations are (1, 3), (2, 3), (3, 1), and (3, 2).
So, P(X = 3)
For X = 4, the possible observations are (1, 4), (2, 4), (3, 4), (4, 3), (4, 2), and (4, 1).
So, P(X = 4)
For X = 5, the possible observations are (1, 5), (2, 5), (3, 5), (4, 5), (5, 4), (5, 3), (5, 2), and (5, 1).
So, P(X = 5)
For X = 6, the possible observations are (1, 6), (2, 6), (3, 6), (4, 6), (5, 6), (6, 4), (6, 3), (6, 2), and (6, 1).
So, P(X = 6)
Therefore, the required probability distribution is as follows:
|
X |
2 |
3 |
4 |
5 |
6 |
|
P(X) |
|
|
|
|
|
Then, E(X) = Σ Xi × P(Xi)