Question

One hundred cards are numbered from $1$ to $100$. The probability that a card chosen at random has the digit $5$ is

• A. $\frac{19}{100}$
• B. $\frac{100}{19}$
• C. $\frac{10}{100}$
• D. $\frac{5}{100}$

Answer 1

Answer: (A)

$\frac{19}{100}$

Cards are numbered from $1$ to $100$

All the numbers from $50$ to $59$ have the digit $5$. They are $9$ in count.
Besides these numbers,the numbers $5,15,25,35,45,65,75,85,95$ have the digit $5$. They are $9$ in count.

$\therefore$ Number of favourable cases $=m=$ Number of numbers which have the digit $5$ $=10+9=19$

Total number of cases $=100$

$\therefore$ Probability, $p=\frac{m}{n}=\frac{19}{100}$

Hence, option A.