Two numbers are selected at random (without replacement) from the first six positive integers Let X denotes the larger - Maths - Probability

Question

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)

Gopal Mohanty · Accepted Answer

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)

For X = 3, the possible observations are (1, 3), (2, 3), (3, 1), and (3, 2)

For X = 4, the possible observations are (1, 4), (2, 4), (3, 4), (4, 3), (4, 2), and (4, 1)

For X = 5, the possible observations are (1, 5), (2, 5), (3, 5), (4, 5), (5, 4), (5, 3), (5, 2), and (5, 1)

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)

Therefore, the required probability distribution is as follows X 2 3 4 5 6 P(X)

X	2	3	4	5	6
P(X)

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).