Question 11
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
a square number
a multiple of 7
Numbers on card = 11, 12, 13, 14, 15, ……… 123
Theory
Numbers between 1 & 3 (including 1 and 3) = 1, 2, 3
∴ Total Numbers = 3
Writing in formula
∴ Total Numbers = 3 – 1 + 1 = 3
Numbers between 5 & 10 (including 5 and 10) = 5, 6, 7, 8, 9, 10
∴ Total Numbers = 6
Writing in formula
∴ Total Numbers = 10 – 5 + 1 = 6
Total cards = 123 – 11 + 1 = 113
(i) Number is a square number
Square numbers = 12, 22, 32, 42, 52, 62, 72, 82, 92, 102, 112, 122,….
Square numbers = 1, 4, 9, 16, 25, 36, 49, 64, 81, 100, 121, 144, …
Square numbers between 11 & 123 = 16, 25, 36, 49, 64, 81, 100, 121
Number of possible numbers = 8
Theory
Square numbers are square of some number.
Eg: 12 = 1, 22 = 4, 32 = 9, 42 = 16
∴ 1, 4, 9, 16 are square numbers
Probability = (𝑁𝑢𝑚𝑏𝑒𝑟 𝑜𝑓 𝑝𝑜𝑠𝑠𝑖𝑏𝑙𝑒 𝑛𝑢𝑚𝑏𝑒𝑟𝑠)/(𝑇𝑜𝑡𝑎𝑙 𝑛𝑢𝑚𝑏𝑒𝑟𝑠)
Probability = 𝟖/𝟏𝟏𝟑
(ii) Number is a multiple of 7
Multiple of 7 are those numbers which come in table of 7
Theory
7 × 1 = 7
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
7 × 17 = 126

Made by

Davneet Singh

Davneet Singh is a graduate from Indian Institute of Technology, Kanpur. He has been teaching from the past 12 years. He provides courses for Maths and Science at Teachoo.