Question 25 (OR 2nd question) An integer is chosen between 70 & 100, Find the probability that it is (a) a prime number (b) divisible by 7
Since integer is chosen between 70 and 100
Possible numbers to be chosen = 71, 72, 73, 74, …. , 98, 99
Therefore,
Total Numbers = (100 – 70) – 1
= 30 – 1
= 29
a prime number
Now, Prime numbers between 70 and 100 are
71, 73, 79, 83, 89, 97
Total Prime numbers = 6
Therefore,
Probability we have a prime number = (𝑇𝑜𝑡𝑎𝑙 𝑝𝑟𝑖𝑚𝑒 𝑛𝑢𝑚𝑏𝑒𝑟𝑠)/(𝑇𝑜𝑡𝑎𝑙 𝑁𝑢𝑚𝑏𝑒𝑟𝑠)
= 𝟔/𝟐𝟗
(b) divisible by 7
Now, Numbers between 70 and 100 divisible by 7 are
77, 84, 91, 98
Total numbers divisible by 7 = 4
Therefore,
Probability number is divisible by 7 = (𝑇𝑜𝑡𝑎𝑙 𝑛𝑢𝑚𝑏𝑒𝑟𝑠 𝑑𝑖𝑣𝑖𝑠𝑖𝑏𝑙𝑒 𝑏𝑦 7)/(𝑇𝑜𝑡𝑎𝑙 𝑁𝑢𝑚𝑏𝑒𝑟𝑠)
= 𝟒/𝟐𝟗

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.