Question

A box contains $20$ cards numbered from $1$ to $20$. A card is drawn at random from the box. Find the probability that the number on the drawn card is
(i) divisible by $2$ or $3$ (ii) a prime number

Answer 1

Solution(i):

Let $E$ be event of drawing a card with number divisible by $2$ or $3$ from the cards with numbers $1$ to $20$

Numbers divisible by $2$ or $3$ from $1$ to $20=2,3,4,6,8,9,10,12,14,15,16,18,20$

No. of favorable outcomes$=13$

Total no. of possible outcomes $=20$

We know that, Probability $P\left(E\right)$ $=\frac{\text{(No.of favorable outcomes)}}{\text{(Total no.of possible outcomes)}}$$=\frac{13}{20}$

Therefore, the probability that a number on the card selected from numbers $1$ to $20$ divisible by $2$ and $3$ is $\frac{13}{20}$

Solution(ii):

Let $F$ be event of drawing a card with prime number from the cards with numbers $1$ to $20$

Prime numbers from $1$ to $20=2,3,5,7,11,13,17,19$

No. of favorable outcomes$=8$

Total no. of possible outcomes $=20$

We know that, Probability $P\left(F\right)$ $=\frac{\text{(No.of favorable outcomes)}}{\text{(Total no.of possible outcomes)}}$$=\frac{8}{20}=\frac{2}{5}$

Therefore, the probability that a card with prime number is selected from numbers $1,2,3,...,20$ $=\frac{2}{5}$