 Hi and how are you all today? The question says the probability that a student entering a university will graduate is 0.4. Find the probability that out of three students of the university, none will graduate, only one will graduate and thirdly all will graduate. So here let us proceed with the solution one by one. We are given the probability that a student will graduate from a university is given to us as 0.4, right? So that means probability that a student will not graduate will be equal to 1 minus the probability that it will graduate that is 0.6, right? So here let x denote the number of students and x is a binomial variate with parameter that is n equal to 3 and p equal to 2 by, now for the first one we need to answer that probability that none will graduate that means x is equal to 0 that will be 3 c0 2 by 5 raised to the power 0 so we are left with 3 by 5 raised to the power 3 minus 0 that is further equal to 3 by 5 raised to the power 2 this is 0. So further we have sorry 3 so we have the answer as 27 that is 3 q divided by 5 cube that is 125 so this is the answer to the first part. Further for the second part we need to find out that only one will graduate that means x is equal to 1 so we have 3 c1 2 by 5 raised to the power 1 divided multiplied by 3 by 5 raised to the power 3 minus 1 that is equal to 3 into 2 by 5 into 3 by 5 the whole square and that comes out to be 54 by 125 after simplification. So this is the answer to the second part. Proceeding with the third part we need to find out that all will graduate that means x is equal to 3 isn't it so it is 3 c3 2 by 5 raised to the power 3 3 by 5 raised to the power 3 minus 3 so we have it as 2 by 5 raised to the power 3 that is equal to 8 by 125 so this is the answer to the last and final part. This completes the session 2 hope you understood it well and enjoyed it too have a nice day ahead.