Question

A box contains cards numbered $3,5,7,9,.....35,37$. A card is drawn at random from the box. Find the probability that the number on the drawn card is a prime number.

Answer 1

Let $E$ be the event of getting a prime number in the event of drawing a card numbered $3,5,7,\mathrm{9.....},37$from the box

Prime numbers from $3$ to $37$$=3,5,7,11,13,17,19,23,29,31,37$
No. of favorable outcomes$=11$

Total no. of possible outcomes $=18$

We know that, Probability $P\left(E\right)$ $=\frac{\text{(No.of favorable outcomes)}}{\text{(Total no.of possible outcomes)}}$$=\frac{11}{18}$

Therefore, the probability that the drawn ticket bears a prime number is $=\frac{11}{18}$