**Question:**

Cards, marked with numbers 5 to 50, are placed in a box and mixed thoroughly. A card is drawn from the box at random. Find the probability that the number on the card is

(i) a prime number less than 10

(ii) a perfect square.

**Solution:**

All possible outcomes are 5, 6, 7, 8...................50.

(i)

Out of the given numbers, the prime numbers less than 10 are 5 and 7.

Let E1 be the event of getting a prime number less than 10.

Then, number of favourable outcomes = 2

$\therefore P$ (getting a prime number less than 10$)=\frac{2}{46}=\frac{1}{23}$

(ii)

Out of the given numbers, the perfect squares are 9, 16, 25, 36 and 49.

Let E2 be the event of getting a perfect square.

Then, number of favourable outcomes = 5

$\therefore P$ (getting a perfect square) $=\frac{5}{46}$