 Good morning friends. I am Purva and today we will discuss the following 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 the problem is solved. 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. This is given to us and let B be the event that B solves the problem then probability of B is equal to 1 upon 3. This is also given to us. Now since A and B are solving specific problem independently so the probability that problem is solved is given by probability that A solves the problem or B solves the problem or both solves the problem. So we have to find probability of A or B or both solving the problem because we have A is the event that A solves the problem and B is the event that B solves the problem. That is we have to find probability of A union B. Now we know that probability of A union B is equal to probability of A plus probability of B minus probability of A intersection B. We mark this as 1. Now A and B are independent events because in the question we are given that both try to solve the problem independently and 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. So since A and B are independent events therefore we have probability of A intersection B is equal to probability of A into probability of B. This is equal to probability of A which is equal to 1 upon 2 into probability of B which is equal to 1 upon 3 and we get this is equal to 1 upon 6. So from equation 1 we have probability of A union B is equal to probability of A that is 1 upon 2 plus probability of B that is 1 upon 3 minus probability of A intersection B which is equal to 1 upon 6 and this is equal to 2 upon 3. So we have got our answer as 2 upon 3. Hope you have understood the solution. Bye and take care.