Let sample space be S = {(1, 2), (1, 3), (1, 4), (1, 5), (1, 6), (2, 1), (2, 3), (2, 4), (2, 5), (2, 6), (3, 1), (3, 2), (3, 4), (3, 5), (3, 6), (4, 1), (4, 2), (4, 3), (4, 5), (4, 6), (5, 1), (5, 2), (5, 3), (5, 4), (5, 6), (6, 1), (6, 2), (6, 3), (6,4), (6, 5)}
Let X denote the random variable, which represents the larger of the two number from first six positive integers.
∴ X can assumes values 2, 3, 4, 5, 6.
[∵ 1 can’t be greater than any other selected number]
∴ P(X = 2) = P({1, 2}, {2, 1}) = P(2 and a number less than 2) =

2

30

P(X = 3) = P((1, 3),(3, 1),(2, 3), (3, 2)) =

4

30

P(X = 4) = P((1, 4), (2, 4), (3, 4), (4, 1), (4, 2), (4, 3)) =

6

30

P(X = 5) = P((1, 5), (2, 5), (3, 5), (4, 5), (5, 1), (5, 2), (5, 3), (5, 4)) =

8

30

And P(X = 6) = P((1, 6),(2, 6), (3, 6), (4, 6), (5, 6), (6, 1), (6, 2), (6, 3), (6, 4), (6, 5)) =

10

30

Hence, the probability distribution is