Question

A box contains $100$ tickets numbered $1,2,3,...,100$. Two tickets are chosen at random. It is given that the maximum number on the two chosen tickets is not more than $10$. The minimum number on them is $5$, with probability.

• A. $\frac{1}{9}$
• B. $\frac{2}{11}$
• C. $\frac{3}{19}$
• D. None

Answer 1

The correct option is A $\frac{1}{9}$

Given that maximum number on the two chosen tickets

is not more than 10.

So, 2 tickets are from 1, 2, 3, 4, 5, 6, 7, 8, 9, 10

Total number of possibilities = ${}^{10}{C}_2=45$

The possibilities with 5 as minimum number are (5,6),

(5, 7), (5, 8), (5, 9) and (5, 10).

So, 5 possibilities.

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