A box contains cards numbered 3, 5, 7, 9, .... , 35, 37. A card is drawn at random from the box.

Given numbers 3, 5, 7, 9, .... , 35, 37 form an AP with a = 3 and d = 2.
Let Tn = 37. Then,
3 + (n − 1)2 = 37
⇒ 3 + 2n − 2 = 37
⇒ 2n = 36
⇒ n = 18

Thus, total number of outcomes = 18.

​Let E be the event of getting a prime number.

Out of these numbers, the prime numbers are 3, 5, 7, 11, 13, 17, 19, 23, 29, 31 and 37.

Number of favourable outcomes = 11.

$\therefore \mathrm{P}$ (getting a prime number) $=\mathrm{P}(\mathrm{E})=\frac{\text { Number of outcomes favourable to } \mathrm{E}}{\text { Number of all possible outcomes }}$

$=\frac{11}{18}$

Thus, the probability that the number on the card is a prime number is $\frac{11}{18}$.