Question

Cards numbered $1$ to $30$ are put in a bag. A card is drawn at random from this bag. Find the probability that the number on the drawn card is
(i) not divisible by $3$ (ii) a prime number greater than $7$ (iii) not a perfect square number

Answer 1

Solution(i):

Let $E$ be the event of drawing a number not divisible by $3$ from the cards numbered $1$ to $30$

Numbers not divisible by $3$ from $1$ to $30=1,2,4,5,7,8,10,11,13,14,16,17,19,20,22,23,25,26,28,29$
No. of favorable outcomes$=20$

Total no. of possible outcomes $=30$

We know that, Probability $P\left(E\right)$ $=\frac{\text{(No.of favorable outcomes)}}{\text{(Total no.of possible outcomes)}}$$=\frac{20}{30}$$=\frac{2}{3}$

Therefore, the probability of drawing a number not divisible by $3$ from the cards numbered $1$ to $30$$=\frac{2}{3}$

Solution(ii):

Let $F$ be the event of drawing a prime number greater than $7$ from the cards numbered from $1$ to $30$

Prime numbers greater than $7$from $1$ to $30=11,13,17,19,23,29$

No. of favorable outcomes$=6$

Total no. of possible outcomes $=30$

We know that, Probability $P\left(F\right)$ $=\frac{\text{(No.of favorable outcomes)}}{\text{(Total no.of possible outcomes)}}$$=\frac{6}{30}$$=\frac{1}{5}$

Therefore, the probability of drawing a prime number greater than $7$ from the cards numbered $1$ to $30$$=\frac{1}{5}$

Solution(iii):

Let $G$ be the event of drawing a non-perfect square number from the cards numbered from $1$ to $30$

Non-Perfect square numbers from $1$ to $30=2,3,5,6,7,8,10,11,12,13,14,15,17,18,19,20,21,22,23,24,26,27,28,29,30$
No. of favorable outcomes$=25$

Total no. of possible outcomes $=30$

We know that, Probability $P\left(G\right)$ $=\frac{\text{(No.of favorable outcomes)}}{\text{(Total no.of possible outcomes)}}$$=\frac{25}{30}$$=\frac{5}{6}$

Therefore, the probability of drawing a non-perfect square number from the cards numbered $1$ to $30$$=\frac{5}{6}$