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. $\frac{1}{8}$
• B. $\frac{13}{15}$
• C. $\frac{1}{7}$
• D. None of these

Answer 1

The correct option is D

None of these

Explanation for the correct option:

Step 1: Express the given data:

The number of tickets is from $1,2,3,......,100$

The event is choosing two tickets.

It is given that the maximum number on the chosen tickets is not more than $10$.

So the sample space is $\left\{1,2,3,4,5,6,7,8,9,10\right\}$

Number of possibilities $={}^{10}C_2$

$=45$

Step 2: Finding the probability:

The minimum number on the tickets is $5$.

The event of choosing two tickets with minimum as $5$ and maximum as $10$ = $\left\{\left(5,6\right),\left(5,7\right),\left(5,8\right),\left(5,9\right),\left(5,10\right)\right\}$

Number of possibilities = $5$

Thus the required probability is

$$\begin{gathered} =\frac{5}{45} \\ =\frac{1}{9} \end{gathered}$$

Hence, Option (D) is the correct answer.