 Hello and welcome to the session. Let us discuss the following question. It says, the probability that a student will pass the final examination in both English and Hindi is 0.5 and the probability of passing neither is 0.1. If the probability of passing the English examination is 0.75, what is the probability of passing Hindi examination? Before moving on to the solution, we will be writing some results. If we have two events, not A and not B. Not A is denoted by A dash and M stands for the intersection, not B is B dash. So A dash intersection B dash is equal to A union B whole dash. This is by the B Morgan's law. So the probability of not A and not B is equal to probability of A union B whole dash that is not A union B. And we know that probability of the complement of any event is 1 minus the probability of that event. So it becomes 1 minus probability of A union B. Also we will be using the result. It says probability of A union B is probability of A plus probability of B minus probability of A intersection B. So this knowledge will work as the ideal. Let us now start the solution and let A be the event of passing English examination. B is the event of passing Hindi examination. Now we are given that probability of passing English examination is 0.75. So probability of A is 0.75 and we are given that probability of passing in both the examination is 0.5. So we are given the probability of passing in both the examination that is passing in A and B. That is passing in English and Hindi both. So we have to find, we are given that probability of A intersection B is 0.5 and we are given the probability passing neither examinations that is not A and not B, 0.1. We have to find the probability of passing in the examination. So we have to find probability of B. Now we can find out probability of B by this formula. Since we are given probability of A intersection B we are given probability of A but we are not given probability of A union B. But we can find out probability of A union B by this formula. That is probability of A union B is equal to 1 minus probability of not A not B. Since here probability of not A and not B is 1 minus probability of A union B. So probability of A union B is equal to 1 minus probability of not A which is denoted by A dash and not B. And here intersection stands for and. So probability of A union B is equal to 1 minus probability of not A and not B which is 0.1. So the probability is equal to 0.9. Now probability of A union B is equal to probability of A plus probability of B minus probability of A intersection B. So this implies probability of B is equal to probability of A union B plus probability of A intersection B minus probability of A. Now substitute probability of A union B which is 0.9 probability of A intersection B is 0.5. Probability of A is 0.75 and this is equal to 0.65. So the probability of passing in the examination is 0.65. So this completes the question and the session. Bye for now. Take care. Have a good day.