Question

A box contains 100 cards marked with number 1 to 100. If one card is drawn randomly from the box.Find the probability that it bears.
(1) Even prime number
(2) A number divisible by 7
(3) The number at unit place is 9.

Answer 1

Total number of outcome $=100$

Prime numbers from $1$ to $100$ are

$2,3,5,7,11,13,17,19,23,29,31,37,41,43,47,53,59,61,67,71,73,79,83,89,97$

Total number of cards with even prime numbers $=1=x$

Numbers divisible by $7$ from $1$ to $100$ are

$7,14,21,28,35,42,47,56,63,70,77,84,91,98$

Total number of cards divisible by $7=14=y$

Numbers with 9 at units place from $1$ to $100$ are

$9,19,29,39,49,59,69,79,89,99$

Total number of cards with $9$ at units place $=10=z$

1) Probability of an even number $=\frac{\text{Total number of cards with even number}}{\text{Total outcomes}}=\frac{x}{100}=\frac{1}{100}=0.01$

2) Probability of number divisible by $7$ $=\frac{\text{Total number of cards with number divisible by 7}}{\text{Total outcomes}}=\frac{y}{100}=\frac{14}{100}$

3) Probability of number having $9$ at units place $=\frac{\text{Total number of cards with 9 at units place}}{\text{Total outcomes}}=\frac{z}{100}=\frac{10}{100}$