The probabilities that a student passes in mathematics, physics and...

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The probabilities that a student passes in mathematics, physics and chemistry are \( \mathrm{m}, \mathrm{p} \) and \( \mathrm{c} \) respectively. Of these subjects, a student has a \( 75 \% \) chance of passing in at least one, a \( 50 \% \)
\( \mathrm{P} \) chance of passing in at least two, and a \( 40 \% \) chance of passing in exactly two subjects. Which of the following relations are true?
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(a) \( p+m+c=\frac{19}{20} \)
(b) \( p+m+c=\frac{27}{20} \)
(c) \( \mathrm{pmc}=\frac{1}{10} \)
(d) \( \mathrm{pmc}=\frac{1}{4} \)
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