Question

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?
1. 13/90
2. 12/90
3. 78/90
4. 77/90

Answer 1

Correct Answer - Option 4 : 77/90

Explanation:

The sample space for the event is (S) = 90 (i.e. from 10 to 99)

2-digit integers divisible by 7 = 14, 21, 28,..................91, 98.

i.e. Total 2-digit integers divisible by 7 = 13

∴ Total 2-digit integers not divisible by 7 = 90 - 13 = 77

∴ Required Probability =  \(\frac{Desired~Outcome}{Sample~Space}\) =  \(\frac{77}{90}\)