The probabilities that a student passes in mathematics, physics and chemistry are m, p and c respectively of these subjects the students has 75%  chance of passing in at least one, a 50% chance of passing in at least two, and a 40% chance of passing in exactly two. Which of the following
relations are true?

We have $\mathrm{P}(\mathrm{A}\cup \mathrm{B}\cup \mathrm{C})=\frac{3}{4}$
$\begin{array}{l}\mathrm{I}.\mathrm{e}, \mathrm{P}\left(\mathrm{A}\right)+\mathrm{P}\left(\mathrm{B}\right)+\mathrm{P}\left(\mathrm{C}\right)-\mathrm{P}(\mathrm{A}\cap \mathrm{B})\\ -\mathrm{P}(\mathrm{B}\cap \mathrm{C})-\mathrm{P}(\mathrm{C}\cap \mathrm{A})+\mathrm{P}(\mathrm{A}\cap \mathrm{B}\cap \mathrm{C})⟶\left(\mathrm{i}\right)\end{array}$
$\mathrm{P}(\mathrm{A}\cap \mathrm{B})+\mathrm{P}(\mathrm{B}\cap \mathrm{C})+\mathrm{P}(\mathrm{A}\cap \mathrm{C})$
 $-2\mathrm{P}(\mathrm{A}\cap \mathrm{B}\cap \mathrm{C})=\frac{1}{2}⟶\left(\text{ ii }\right)$
And $\mathrm{P}(\mathrm{A}\cap \mathrm{B})+\mathrm{P}(\mathrm{B}\cap \mathrm{C})+\mathrm{P}(\mathrm{A}\cap \mathrm{C})$
$-3\mathrm{P}(\mathrm{A}\cap \mathrm{B}\cap \mathrm{C})=\frac{2}{5}⟶\left(\text{ iii }\right)$
From eq’s (ii) and (iii) we get
$\begin{array}{l}\mathrm{P}(\mathrm{A}\cap \mathrm{B}\cap \mathrm{C})=\frac{1}{2}-\frac{2}{5}=\frac{1}{10}⟶\left(\mathrm{iv}\right)\\ \mathrm{P}\left(\mathrm{A}\right)\mathrm{P}\left(\mathrm{B}\right)\mathrm{P}\left(\mathrm{C}\right)=\frac{1}{10}\\ \mathrm{PMC}=\frac{1}{10}\end{array}$
From eq’s (i) ,(ii) and (iii) we have
$\begin{array}{l}\mathrm{P}\left(\mathrm{A}\right)+\mathrm{P}\left(\mathrm{B}\right)+\mathrm{P}\left(\mathrm{C}\right)-\left(\frac{1}{2}+\frac{2}{10}\right)+\frac{1}{10}=\frac{3}{4}\\ \mathrm{P}+\mathrm{m}+\mathrm{c}=\frac{27}{20}\end{array}$