Question

There are 100 flash cards labelled from 1 to 100 in a bag. When a card is drawn from the bag at random, what is the probability of getting?
$\left( i \right)$A card with prime number from possible outcomes.
$\left( {ii} \right)$A card without prime number from possible outcomes.

Answer 1

Hint: - Probability$\left( P \right) = \dfrac{{{\text{Favorable number of cases}}}}{{{\text{Total number of cases}}}}$
Prime numbers from 1 to 100 are
$\left\{ {2,3,5,7,11,13,17,19,23,29,31,37,41,43,47,49,53,59,61,71,73,79,83,89,97} \right\}$
Prime numbers are those whose factors are either 1 or itself.
Total numbers from 1 to 100$ = 100$
And total prime numbers from 1 to 100$ = 25$(Favorable cases)
As we know that probability$\left( P \right) = \dfrac{{{\text{Favorable number of cases}}}}{{{\text{Total number of cases}}}}$
$\left( i \right)$A card with prime number from possible outcomes.
Therefore probability of getting a prime number is$\left( P \right) = \dfrac{{{\text{Favorable number of cases}}}}{{{\text{Total number of cases}}}} = \dfrac{{25}}{{100}} = \dfrac{1}{4}$
$\left( {ii} \right)$A card without prime number from possible outcomes.
As we know total probability is 1
Therefore probability of not getting a prime number$ = 1 - $probability of getting a prime number
$ = 1 - \dfrac{1}{4} = \dfrac{3}{4}$
So, this is the required probability.

Note: - In such types of questions first find out the total numbers, then find out the number of favorable cases, then divide them using the formula which is stated above, we will get the required answer.