 Good morning friends. I am Poohran. Today we will work out the following question. Events A and B are such that probability of A is equal to 1 upon 2, probability of B is equal to 7 upon 12 and probability of not A or not B is equal to 1 upon 4. State whether A and B are independent. Now if E and F are two independent events then we have probability of E intersection F is equal to probability of E into probability of F. So this is the key idea behind our question. Let us begin with the solution now. Now we are given that probability of A is equal to 1 upon 2, probability of B is equal to 7 upon 12 and probability of not A or not B is equal to 1 upon 4. Now we know that not A or not B means A complement union B complement so we get probability of not A or not B is equal to probability of A complement union B complement. Also we know that A complement union B complement is equal to A intersection B whole complement so we get probability of A complement union B complement is equal to probability of A intersection B whole complement and we also know that probability of A intersection B whole complement is equal to 1 minus probability of A intersection B or we can say probability of A intersection B is equal to 1 minus probability of A intersection B whole complement and this is equal to 1 minus probability of A intersection B whole complement is equal to probability of A complement union B complement which is equal to probability of not A or not B and this is given to be 1 upon 4. So we have 1 minus 1 upon 4 so we get probability of A intersection B is equal to 3 upon 4 we mark this as 1. Now probability of A into probability of B is equal to probability of A is equal to 1 upon 2 this is given to us and probability of B is equal to 7 upon 12 this is also given to us and this is equal to 7 upon 24. So we have got probability of A into probability of B is equal to 7 upon 24 we mark this as 2. Now 1 and 2 we have probability of A intersection B is not equal to probability of A into probability of B. Now by key idea we know that for two independent events E and F probability of E intersection F is equal to probability of E into probability of F. Now here we have got probability of A intersection B is not equal to probability of A into probability of B. So this implies A and B are not independent so we have got our answer as A and B are not independent. Hope you have understood the solution. Bye and take care.