Question 17354 – NTA UGC NET Dec 2023 Paper-2

The set of positive integers not exceeding 100 can be represented as {1, 2, 3, …, 100}.
To find the probability that a randomly selected positive integer from this set is divisible by either 2 or 5, we need to find the count of numbers divisible by 2 or 5 and divide it by the total count of numbers.
Count of numbers divisible by 2: 1, 2, 3, …, 100 Count = 100/2 = 50
Count of numbers divisible by 5: 5, 10, 15, …, 100
Count = 100/5 = 20
However, numbers divisible by both 2 and 5 (i.e., divisible by 10) have been counted twice, so we need to subtract them once.
Count of numbers divisible by 10: 10, 20, 30, …, 100
Count = 100/10 = 10
Now, apply the inclusion-exclusion principle:
Total count = Count of numbers divisible by 2 + Count of numbers divisible by 5 – Count of numbers divisible by 10 = 50 + 20 – 10 = 60
Probability = (Count of favorable outcomes) / (Total count) = 60 / 100
Simplify the fraction: Probability = 3/5