**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 card is a prime number.

**Solution:**

Given numbers 3, 5, 7, 9, .... , 35, 37 form an AP with *a* = 3 and *d* = 2.

Let *T**n* = 37. Then,

3 + (*n* − 1)2 = 37

⇒ 3 + 2*n* − 2 = 37

⇒ 2*n* = 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 $\frac{11}{18}$.