Answer :

Given that, the probability that a student entering a university will graduate is 0.4.


Let p be the probability that a student entering a university will graduate.


p = 0.4




Then, q is the probability of a student not graduating.


But, p + q = 1


q = 1 – p





Let X be a random variable that represents the number of students out of n students graduating after entering a university.


Then, the probability of r students out of n students graduating after entering a university is given by,


P (X = r) = nCrprqn-r


Here, a sample size of students, n = 3


Putting the value of n, p, and q in the above formula, we get


…(A)


(i). We need to find the probability that out of 3 students entering a university, none will graduate.


Put r = 0 in equation (A). We get







, the probability that none will graduate is 0.216.


(ii). We need to find the probability that out of 3 students only 1 will graduate.


So, put r = 1 in equation (A). We get








P (X = 1) = 0.432


, the probability that exactly one will graduate is 0.432.


(iii) We need to find the probability that out of 3 students all will graduate.


So, put r = 3 in equation (A). We get






P (X = 3) = 0.064


, the probability that all will graduate is 0.064.


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