Question

The probability that a student entering a university will graduate is 0.4. Find the probability that out of 3 students of the university
(i) none will graduate
(ii) only one will graduate
(iii) all will graduate

Answer 1

Let X be the number of students that graduate from among 3 students.
Let p=probability that a student entering a university will graduate.

Here , n =3, p=0.4 and q = 0.6
Hence, the distribution is given by
$P(X=r)={}^{3}C_r{\left(0.4\right)}^r{\left(0.6\right)}^{3-r},r=0,1,2,3$

$$\begin{gathered} \left(\mathrm{i}\right)P(X=0)=\mathit{}{q}^3=0.216 \\ \left(\mathrm{ii}\right)\mathit{}P(X=1)=3(0.4)(0.36)=0.432 \\ \left(\mathrm{iii}\right)P(X=3)=\mathit{}{p}^3=0.064 \end{gathered}$$