Question

A box contains 100 cards marked with numbers 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

There are 100 cards in the box marked with number 1 to 100.

A card is drawn randomly from it.

$\therefore$ Number of possible outcomes = $100$

(1) Let A be the event that the card bears an even prime number.

There is only 1 even prime number from 1 to 100, that is '2'.

$\therefore$ The number of outcomes favourable to A is 1.

$\therefore P\left(A\right)=\frac{1}{100}=0.01$

(2) Let B be the event that the card bears a number divisible by 7.

Numbers divisible by 7 from 1 to 100 are

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

There are 13 multiples of 7 from the numbers 1 to 100.

$\therefore$ The number of outcomes favourable to B is 13.

$\therefore P\left(A\right)=\frac{13}{100}=0.13$

(3) Let be the event that the card bears a number that has 9 at the unit place.

The numbers from 1 to 100 that have 9 at the units place are

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

There are 10 numbers that have 9 at the unit place.

$\therefore$ The number of outcomes favourable to C is 10.

$\therefore P\left(A\right)=\frac{10}{100}=0.1$