A box contains 100 tickets numbered 1 to 100. Two tickets are chosen at random. It is given that the maximum number on them is not more than 10. The minimum number on them is 5 with probability

The two numbers with maximum $\le 10$ are$(1, 2),(1, 3), (1, 4)\dots \dots (1, 10),(2, 3), (2, 4)\dots \dots (2, 10), (3, 4)\dots \dots (3, 10)\dots \dots (9, 10)$

$1+2+3+\dots \dots +9=45$ number pairs of these

$(5,6),(5,7),(5,8),(5,9),(5,10)$ have minimum 5.

$\therefore$ The desired probability $=\frac{5}{45}=\frac{1}{9}$.