Question

Cards numbered from $11$ to $60$ are kept in a box. If a card is drawn at random from the box, find the probability that the number on the drawn card is
(i) an odd number (ii) a perfect square number (iii) divisible by $5$ (iv) a prime number less than $20$

Answer 1

Solution(i):

Let $E$ be the event of drawing a number from the cards numbered from $11$ to $60$

Odd numbers from $11$ to $60=11,13,15,.....,89$
No. of favorable outcomes$=25$

Total no. of possible outcomes $=50$

We know that, Probability $P\left(E\right)$ $=\frac{\text{(No.of favorable outcomes)}}{\text{(Total no.of possible outcomes)}}$$=\frac{25}{50}$$=\frac{1}{2}$

Therefore, the probability of an odd number from the cards numbered $11$ to $60$$=\frac{1}{2}$

Solution(ii):

Let $F$ be the event of drawing a perfect square number from the cards numbered from $11$ to $60$

Perfect square numbers from $11$ to $60=16,25,36,49$
No. of favorable outcomes$=4$

Total no. of possible outcomes $=50$

We know that, Probability $P\left(F\right)$ $=\frac{\text{(No.of favorable outcomes)}}{\text{(Total no.of possible outcomes)}}$$=\frac{4}{50}$$=\frac{2}{25}$

Therefore, the probability of drawing a perfect square number from the cards numbered from $11$ to $60$$=\frac{2}{25}$

Solution(iii):

Let $G$ be the event of drawing a number divisible by $5$ from the cards numbered from $11$ to $60$

Numbers divisible by $5$ from $11$ to $60=15,20,25,30,35,40,45,50,55,60$
No. of favorable outcomes$=10$

Total no. of possible outcomes $=50$

We know that, Probability $P\left(G\right)$ $=\frac{\text{(No.of favorable outcomes)}}{\text{(Total no.of possible outcomes)}}$$=\frac{10}{50}$$=\frac{1}{5}$

Therefore, the probability of drawing a number divisible by $5$ from the cards numbered from $11$ to $60$$=\frac{1}{5}$

Solution(iv):

Let $H$ be the event of drawing a prime number less than $20$ from the cards numbered from $11$ to $60$

Prime numbers less than $20$ from $11$ to $60=11,13,17,19$
No. of favorable outcomes$=4$

Total no. of possible outcomes $=50$

We know that, Probability $P\left(H\right)$ $=\frac{\text{(No.of favorable outcomes)}}{\text{(Total no.of possible outcomes)}}$$=\frac{4}{50}$$=\frac{2}{25}$

Therefore, the probability of drawing a prime number less than $20$ from the cards numbered from $11$ to $60$$=\frac{2}{25}$