Question

Out of 100 students, two sections of 40 and 60 are formed. If you and your friend are among 100 students, what is the probability that: (i) you both enter the same section? (ii) you both enter the different sections?

Answer 1

$$\begin{gathered} \left(\mathrm{i}\right)P\left(\text{both enter same section}\right)=P\left(\text{both enter section A}\right)+P\left(\text{both enter section B}\right) \\ =\frac{40}{100}\times \frac{40}{100}+\frac{60}{100}\times \frac{60}{100} \\ =\frac{4}{25}+\frac{9}{25} \\ =\frac{13}{25} \\ \left(\mathrm{ii}\right)P\left(\text{both enter different sections}\right)=1-P\left(\text{both enter same section}\right) \\ =1-\frac{13}{25} \\ =\frac{12}{25} \end{gathered}$$