 Hi friends, I am Pooja and today we will discuss the following question. In a hostel, 60% of the students read Hindi newspaper, 40% read English newspaper and 20% read both Hindi and English newspapers. A student is selected at random. If she reads English newspaper, find the probability that she reads Hindi newspaper. Now the conditional probability of an event E given the occurrence of the event F is given by probability of E given F is equal to probability of E intersection F upon probability of F and her probability of F is not equal to 0. So this is the key idea behind our question. Let us begin with the solution now. Now in the question we have, if she reads English newspaper, find the probability that she reads Hindi newspaper. So let E be the event that she reads Hindi newspaper. Then probability of E is equal to 60 upon 100 because we are given that 60% of the students read Hindi newspaper. And this is equal to 3 upon 5 and let F be the event that she reads English newspaper. Then we have probability of F is equal to 40 upon 100 because we are given that 40% of the students read English newspaper and this is equal to 2 upon 5. Now we are also given that 20% of the students read both Hindi and English newspapers. So probability of E intersection F that is probability that she reads both newspapers is equal to 20 upon 100 and this is equal to 1 upon 5. In the question we have, a student is selected at random. If she reads English newspaper, find the probability that she reads Hindi newspaper. So we have to find probability of E provided F has happened that is we have to find probability of E given F. Now by key idea we know that the conditional probability of an event E given the occurrence of the event F is given by probability of E given F which is equal to probability of E intersection F upon probability of F and here probability of F is not equal to 0. So probability of E given F is equal to probability of E intersection F upon probability of F this is equal to now probability of E intersection F is equal to 1 upon 5 upon probability of F which is equal to 2 upon 5 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.