Cards numbered from 11 to 60 are kept in a box. If a card is drawn at random from the box, find the probability that the number on the drawn card is:

(i) an odd number

(ii) a perfect square number

(iii) divisible by 5

(iv) a prime number less than 20

Total number of cards = 60 – 11 + 1 = 50

We know that the theoretical (classical) probability of an event E, written as P (E), is defined as P (E) = Number of outcomes favorable to E / Number of all possible outcomes of the experiment

(i) Odd number:

Odd numbers are 11, 13, 15, 17, …, 59 =

25 numbers

P (an odd number) =

(ii) Perfect square number:

Perfect square numbers are 16, 25, 36, and 49 =

4 numbers

P (a perfect square number) =

(iii)Divisible by 5:

“Divisible by 5” numbers are 15, 20, 25, 30, 35, 40, 45, 50, 55, 60, = 10 numbers

P (divisible by 5) =

(iv) Prime numbers less than 20:

Prime numbers less than 20 are 2, 3, 5, 7, 11, 13, 17, 19 = 8 numbers

P (a prime no. less than 20) =