If a positive integer is selected randomly and is divided by 7, what is the probability that the remainder is greater than 0 and NOT an even number?

Explanation: To meet the given condition, the remainders can be 1,3 or 5. Out of every 7 integers, there are 3 integers, which if divided by 7 leave a remainder of 1 or 3 or 5. For example, from 8 to 14, dividing 8, 10,12 will leave remainders of 1,3 and 5 respectively. The general format can be expressed as \(7n+1\), \(7n+3\), and \(7n+5\). Starting from 1 all the way to infinity, we can divide the numbers into groups of 7 positive integers. Here, 3 positive integers will meet the desired condition. So, probability \(=3/7\).