 Hello students, let's solve the following problem of probability. It says in a class of 60 students, 30 opted for NCC, 32 opted for NSS, 24 opted for both NCC and NSS. If one of these students is selected at random, find the probability that student opted for NCC or NSS. The student has opted neither NCC nor NSS. The student has opted NSS but not NCC. Let us now move on to the solution, be the students opted for NSS be the students opted for NCC. Now we are given that 30 students opted for NCC, 32 opted for NSS and 24 opted for both. So the probability of A is equal to 32 upon 60 that is the number of students opted for NSS upon the total number of students. As we know that probability of any event E is the number of outcomes favourable to E upon the total number of outcomes. Similarly probability of B is 30 upon 60 that is the number of students opted for NCC upon the total number of students. And probability of A intersection B that is the number of students opted for both NCC and NSS is 24 by 60. Now in the first part we have to find probability that student opted for NCC or NSS. So we have to find probability of A or B which is same as probability of A union B which is given by probability of A plus probability of B minus probability of A intersection B. Now probability of A is 32 by 60 probability of B is 30 by 60 probability of A intersection B is 24 by 60 which is equal to 38 by 60 which is same as 19 by 30. Now in the second part we have to find the probability that student has opted neither NCC nor NSS that is we have to find probability not A and not B. Now not A is denoted by A dash and stands for intersection so A dash intersection B dash is same as A union B whole dash by the D Morgan's law. So the probability of A dash intersection B dash is equal to the probability of A union B whole dash that is complement of A union B and we know that probability of the complement of any event is 1 minus probability of that event. So the probability of not A and not B is equal to 1 minus probability of A union B so the probability of not A and not B is equal to 1 minus probability of A union B which is 19 by 30 So this is equal to 11 by 30. Now in the third part we have to find the probability that student has opted for NSS but not NCC. So we have to find the probability A but not B because he has opted for NSS but not for NCC. So A not B probability of A and not B or we can say probability of A intersection B dash is given by probability of A minus probability of A intersection B. Now probability of A is 32 by 60 and probability of A intersection B is 24 by 60. This is equal to 8 upon 16 which is equal to 2 upon 15. Hence answer to the first part of the question is 19 upon 30 to the second part answer is 11 upon 30 and to the third part answer is 2 upon 15. So this completes the question and the session. Hope you will be able to solve more of such problems. Bye for now, take care, have a good day.