The probabilities of Rotey obtaining the highest mark in Mathematics, Physics and Biology tests are 0.9, 0.75 and 0.8 respectively. Calculate the probability of getting the highest marks in at least two of the subjects.
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) = \((\frac{9}{10} \times \frac{3}{4} \times \frac{1}{5}) + (\frac{9}{10} \times \frac{4}{5} \times \frac{1}{4}) + (\frac{3}{4} \times \frac{4}{5} \times \frac{1}{10}) + (\frac{9}{10} \times \frac{3}{4} \times \frac{4}{5})\) = \(\frac{27}{200} + \frac{36}{200} + \frac{12}{200} + \frac{108}{200}\) = \(\frac{183}{200}\) = \(0.915\)
