Question

Probabilities that Rajesh passes in Physics, Math and Chemistry
are p, m and c respectively. Of these subjects, Rajesh has
75% chance of passing in at least one, 50% chance of passing
in at least two and 40% chance of passing in exactly two. Find
which of the following is true.

Answer 1

\(\large \color{black}{\begin{align}
& \normalsize \text{Probabilities that Rajesh passes in Physics, Math and Chemistry }\hspace{.33em}\\~\\
& \normalsize \text{are p, m and c respectively. Of these subjects, Rajesh has }\hspace{.33em}\\~\\
& \normalsize \text{75% chance of passing in at least one, 50% chance of passing}\hspace{.33em}\\~\\
& \normalsize \text{in at least two and 40% chance of passing in exactly two. Find}\hspace{.33em}\\~\\
& \normalsize \text{which of the following is true.}\hspace{.33em}\\~\\
& a.)\ p+m+c=\dfrac{19}{20} \hspace{.33em}\\~\\
& b.)\ p+m+c=\dfrac{27}{20} \hspace{.33em}\\~\\
& c.)\ pmc=\dfrac{1}{20} \hspace{.33em}\\~\\
& d.)\ pmc=\dfrac18 \hspace{.33em}\\~\\
\end{align}}\)

Answer 2

i found this but cant understand the answer

https://math.stackexchange.com/questions/1422953/probability-problem-possibly-based-on-principle-of-inclusion-exclusion

Answer 3

Yes, principle of inclusion and exclusion is your answer.
Let's start with a venn diagram so that we're on the same wavelength.