 Hi friends, I am Purva and today we will discuss the forward question, probability of solving specific problem independently by A and B are 1 upon 2 and 1 upon 3 respectively. If both try to solve the problem independently, find the probability that exactly one of them solves the problem. Now if E and F are 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 in the question we are given that probability of solving specific problem independently by A and B are 1 upon 2 and 1 upon 3 respectively. So let A be the event that A solves the problem. Then we have probability of A is equal to 1 upon 2 and let B be the event that B solves the problem. Then we have probability of B is equal to 1 upon 3. Now we have to find the probability that exactly one of them solves the problem. Now exactly one of them solves the problem means A solves the problem and B does not solve the problem or B solves the problem and A does not solve the problem. So we have to find probability of A and not B plus probability of B and not A. Now A and not B means intersection of A and B complement. So probability of A and not B is equal to probability of A intersection B complement. Now by key idea we know that 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. A and B are independent events this is given to us. Now since B is an independent event so B complement is also an independent event so we get this is equal to probability of A into probability of B complement. Now this is equal to probability of A into 1 minus probability of B. Since we know that probability of B complement is equal to 1 minus probability of B this is equal to now probability of A is equal to 1 upon 2 so we have 1 upon 2 into 1 minus probability of B which is equal to 1 upon 3 this is equal to 1 upon 2 into 2 upon 3 because 1 minus 1 upon 3 is equal to 2 upon 3 and this is equal to 1 upon 3. Similarly we have B and not A means intersection of B and A complement so probability of B and not A is equal to probability of B intersection A complement. Now again since A is independent which is given to us so we have A complement is independent also we are given that B is independent so by key idea we have this is equal to probability of B into probability of A complement this is equal to probability of B into 1 minus probability of A since we have probability of A complement is equal to 1 minus probability of A this is equal to probability of B which is equal to 1 upon 3 into 1 minus probability of A which is equal to 1 upon 2 this is equal to 1 upon 3 into 1 upon 2 and this is equal to 1 upon 6. Now we mark this as 1, we mark this as 2 and we mark this as 3. So from 1, 2 and 3 we get probability of A and not B plus probability of B and not A is equal to 1 upon 3 plus 1 upon 6 and this is equal to 1 upon 2. So we have got our answer as 1 upon 2. Hope you have understood the solution. Bye and take care.