Question

There are $30$ cards of same size, in a bag on which numbers $1$ to $30$ are written. One card is taken out of the bag at random. Find the probability that the number on the selected card is not divisible by $3$.

Answer 1

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

The numbers not divisible by 3 upto $30=1,2,4,5,7,8,10,11,13,14,16,17,19,20,22,23,25,26,28,29$
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 that the number on the selected card is not divisible by$3=\frac{2}{3}$