Explanation

\(p(M) = 0.9 = \frac{9}{10} ; p(M') = 0.1 = \frac{1}{10}\)

\(p(P) = 0.75 = \frac{3}{4} ; p(P') = 0.25 = \frac{1}{4}\)

\(p(B) = 0.8  = \frac{4}{5} ; p(B') = 0.2 = \frac{1}{5} \)

p(at least two subjects) = p(Maths and Physics not Biology) or p(Maths and Biology not Physics) or p(Physics and Biology not Maths) or p(all three subjects)

= \((\frac{9}{10} \times \frac{3}{4} \times \frac{1}{5}) + (\frac{9}{10} \times \frac{4}{5} \times \frac{1}{4}) + (\frac{3}{4} \times \frac{4}{5} \times \frac{1}{10}) + (\frac{9}{10} \times \frac{3}{4} \times \frac{4}{5})\)

= \(\frac{27}{200} + \frac{36}{200} + \frac{12}{200} + \frac{108}{200}\)

= \(\frac{183}{200}\)

= \(0.915\)

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