Out of all the 2-digit integers between 1 and 100, a 2-digit number has to be selected at random. What is the probability that the selected number is not divisible by 7? , Out of all the 2-digit integers between 1 and 100, a 2-digit number has to be selected at random. What is the probability that the selected number is not divisible by 7?

Solution

D. 77/90

Explanation

 Solution:
Given: All the 2-digit numbers
To find: Probability of selecting a number at random not divisible by 7
Analysis: Total number of 2-digit numbers
10, 11, …….., 99 → 90 numbers
Unfavourable numbers i.e. numbers divisible b
7 : 14, 21, ………, 98
Number of unfavourable numbers = 13
This can be hand counted or we can use the following properties :
Last term = First time + (no. – 1) Diff
98 = 14 + (no. - 1) 7
⇒ no. = 13
⇒ Probability 

Hence, the solutions is D