Question

Cards marked with numbers $13,14,15,....,60$ are placed in a box and mixed thoroughly. One card is drawn at random from the box. Find the probability that number on the card drawn is
(i) divisible by $5$ (ii) a number is a perfect square

Answer 1

Solution(i):

Let $E$ be event of drawing a card with number divisible by $5$ from the cards marked with numbers $13,14,15,....,60$

Numbers divisible by $5$ from $13$ to $60=15,20,25,30,35,40,45,50,55,60$
No. of favorable outcomes$=10$

Total no. of possible outcomes $=48$

We know that, Probability $P\left(E\right)$ $=\frac{\text{(No.of favorable outcomes)}}{\text{(Total no.of possible outcomes)}}$$=\frac{10}{48}=\frac{5}{24}$

Therefore, the probability that a number on the card selected from numbers $13,14,15,...,60$ divisible by $5$ is $\frac{5}{24}$

Solution(ii):

Let $G$ be event of drawing a card with a perfect square number from the cards marked with numbers $13,14,15,....,60$

Numbers, perfect square, from $13$ to $60=16,25,36,49$
No. of favorable outcomes$=4$

Total no. of possible outcomes $=48$

We know that, Probability $P\left(G\right)$ $=\frac{\text{(No.of favorable outcomes)}}{\text{(Total no.of possible outcomes)}}$$=\frac{4}{48}=\frac{1}{12}$

Therefore, the probability that a card with perfect square number is selected from numbers $13,14,15,...,60$ $=\frac{1}{12}$