Question

The probability of all $3$-digit numbers having all the digits same is

• A. $\frac{1}{100}$
• B. $\frac{3}{100}$
• C. $\frac{7}{100}$
• D. None of these

Answer 1

The correct option is A

$\frac{1}{100}$

Explanation for the correct answer:

Determining the probability of all $3$-digit numbers having all the digits same:

Since the three-digit numbers start from $100$ and end at $999$ the total number of $3$-digit numbers is $900$

The three-digit numbers with all the digits as the same are $\left\{111,222,333,444,555,666,777,888,999\right\}$

The total number of $3$-digit numbers in which all the digits are the same $=9$

Therefore, the required probability is $\frac{\mathrm{Favourable}\mathrm{cases}}{\mathrm{Total}\mathrm{number}\mathrm{of}\mathrm{cases}}$

Therefore, the required probability is,

$\frac{9}{900}=\frac{1}{100}$

Therefore, the correct answer is option (A).