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 probabilit...
Question 1 Report
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.
Answer Details
Let the probabilities of topping be \(M = 0.9,\ P = 0.75,\ B = 0.8\), with complements \(0.1,\ 0.25,\ 0.2\). "At least two" means exactly two or all three.
All three: \(0.9\times0.75\times0.8 = 0.54\).
Exactly two:
- \(M,P\) not \(B\): \(0.9\times0.75\times0.2 = 0.135\)
- \(M,B\) not \(P\): \(0.9\times0.25\times0.8 = 0.180\)
- \(P,B\) not \(M\): \(0.1\times0.75\times0.8 = 0.060\)
Sum of exactly two \(= 0.135 + 0.180 + 0.060 = 0.375\).
\[P(\text{at least two}) = 0.375 + 0.54 = \mathbf{0.915}\]Download The App On Google Playstore
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