 Hi and how are you all today? The question says an integer is chosen at random from the first 200 positive integers. Find the probability that it is divisible by 6 or 8. So let's proceed with the solution. Here let S be the sample space that is n bracket S that is equal to 200. Therefore total number of elementary events will be equal to what? Same as 200. Now A be the event that the number selected is divisible by 6 and therefore let B be the event that the number selected is divisible by 8. So we have elements in A as 6, 12, 18 and so on and the last one is 198. That means number of elements in this event are 98 divided by 6 that is similarly B is having elements as 8, 16, 24 and so on till 200. So number of elements in set B are equal to 200 divided by 8 that is equal to 20. There are few elements that are common in both that are 24, 48, 72 and so on till 190. Number of elements in this sets are equal to 192 divided by 24 that is equal to number of elements in set A upon number of elements in sample space that is 33 upon 200. Similarly probability of B is equal to n of B upon n of S that is equal to 25 upon 200. Probability of their intersection is number of elements in their intersection upon number of elements that are in sample set 8 upon 1200. We need to find out probability that a number is divisible by to probability of their union and that is equal to probability of A plus probability of B minus probability of A intersection B. So it is upon 200 plus 25 upon 200 minus 8 upon 200 minus 8 upon 100 that comes out to be 50 upon 200 that on simplification gives us 1 by 4 that is the answer to this question. So understood it well and enjoyed it. Have a nice day.