 Good morning friends. I am Purva 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 Hindi newspaper, find the probability that she reads English 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 here we have 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 if a student reads Hindi newspaper, we have to find the probability that she reads English newspaper. So let E be the event that she reads Hindi newspaper. Then we have 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. Now 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 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. Now in the question we have a student is selected at random. If she reads Hindi newspaper find the probability that she reads English newspaper. So we have to find probability of F provided E has happened that is we have to find probability of F given E. 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. So probability of F given E is equal to probability of F intersection E upon probability of E and here probability of E is not equal to 0. This is equal to now we know that probability of F intersection E is equal to probability of E intersection F and it is equal to 1 upon 5. So we have 1 upon 5 upon probability of E which is equal to 3 upon 5 and this is equal to 1 upon 3. So we have got our answer as 1 upon 3. Hope you have understood the solution. Bye and take care.