A box contains cards numbered 11 to 123. A card is drawn at random from the box. Find the probability that the number on the drawn card is

(i) a square number

(ii) a multiple of 7

Given: A box containing cards numbered 11 to 123.

Total numbers from 1 to 123 = 123

Total numbers from 1 to 10 = 10

So, total numbers from 11 to 123 = (numbers from 1 to 123) – (numbers from 1 to 10)

= 123 – 10 = 113

⇒ Number of cards the box contain = 113 …(A)

(i). To find the probability that the number on the drawn card is a square number:

We need to find square numbers from 11 to 123.

So, square numbers from 11 to 123 = 4², 5², 6², 7², 8², 9², 10², 11²

i.e., 16, 25, 36, 49, 64, 81, 100, 121 all lie between 11 and 123.

There are total 8 square numbers from 11 to 123. …(B)

Probability(a square numbered card is drawn) =

= [from (A) & (B) statement]

(ii). To find the probability that the number on the drawn card is a multiple of 7:

We need to find multiples of 7 between numbers 11 and 123.

So, multiples of 7 from 11 to 123 = (7 × 2 =) 14, (7 × 3 =) 21, (7 × 4 =) 28, (7 × 5 =) 35, (7 × 6 =) 42, (7 × 7 =) 49, (7 × 8 =) 56, (7 × 9 =) 63, (7 × 10 =) 70, (7 × 11 =) 77, (7 × 12 =) 84, (7 × 13 =) 91, (7 × 14 =) 98, (7 × 15 =) 105, (7 × 16 =)112, (7 × 17 =) 119

i.e., 14, 21, 28, 35, 42, 49, 56, 63, 70, 77, 84, 91, 98, 105, 112, 119 all are multiples of 7 between 11 and 123.

There are total 16 multiples of 7 from 11 to 123.

Probability(multiples of 7 is drawn) =

=