 Hi friends, I am Pulva and today we will work out 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. Find the probability that she reads neither Hindi nor English newspapers. Let us begin with the solution now. Now, in the question we are given that a student is selected at random and we have to find the probability that she reads neither Hindi nor English newspapers. 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 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 have 40% of the students read English newspaper and this is equal to 2 upon 5. Now in the question we are also given that 20% of the students read both Hindi and English newspapers. So we have 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 we have to find the probability that she reads neither Hindi nor English newspapers. Now the probability that she reads Hindi or English newspapers is given by probability of E union F because we have E is the event that she reads Hindi newspaper and F is the event that she reads English newspaper. So probability that she reads neither Hindi nor English newspapers will be given by probability of E union F whole complement. So we have to find probability of E union F whole complement and this is equal to 1 minus probability of E union F. Since we know that probability of A complement is equal to 1 minus probability of A. Now we know that probability of E union F is given by probability of E plus probability of F minus probability of E intersection F. This is equal to now probability of E is equal to 3 upon 5 plus probability of F is equal to 2 upon 5 minus probability of E intersection F is equal to 1 upon 5 and we get this is equal to 4 upon 5. So probability of E union F whole complement which is equal to 1 minus probability of E union F is equal to 1 minus 4 upon 5 and this is equal to 1 upon 5. Thus we have got our answer as 1 upon 5. Hope you have understood the solution. Bye and take care.