 Hi and how are you all today? My name is Priyanka and let us discuss the following question. It says an integer is chosen on random from the first hundred positive integers. Find the probability that the integer is divisible by six or eight. So here let us start the solution to this question. Here the sample space starts from one, two, three and so on till hundred, right? They are the first hundred positive integers. That means number of elements in this sample space is hundred. Further, let E1 be the event of getting a number divisible by six and let E2 be the event of getting a number divisible by eight, right? Then, E1 in the section E2 be the event of getting a number divisible by both six and eight. Now a number which is divisible by both six and eight will be equal to a number divisible by 24, isn't it? Because it is the LCM of six and eight. Also, the elements that will be in event one will be six, 12, 18 and so on till ninety-six, whereas the elements that will be in event two are eight, sixteen, twenty-four and so on till ninety-six. That means number of elements in event one are equal to sixteen and number of elements in event two are equal to twelve. So, E1 intersection E2 are equal to four. Now, let us find out the probability of event one, that is, N of E1 upon number of elements in sample space, that is sixteen upon hundred, that comes out to be four upon twenty-five. Similarly, P of E2 is equal to N E2 divided by Ns, that is, twelve upon hundred, that is, equal to three upon twenty-five. Also, probability of E1 intersection E2 is equal to number of elements that are in this divided by number of elements in sample space, that comes out to be four upon hundred and that is one upon twenty-five. Hence, probability that the integer is divisible by six or eight is equal to probability of E1 union E2, that is probability of E1 plus probability of E2 minus probability of E1 intersection E2. Now, let us substitute the values of probability of E1, E2 and their intersection that we got above, all these three values. That is equal to four upon twenty-five plus three upon twenty-five minus one upon twenty-five. Taking the LCM and adding and subtracting the numerator, we get six upon twenty-five. That is the required answer to the given question. So, hope you understood whole process well and enjoyed it too. Have a nice day ahead.