JEE Advanced 2012 Paper 1 Mathematics Q13

Mathematics

Problem

A ship is fitted with three engines E1E_1, E2E_2 and E3E_3. The engines function independently of each other with respective probabilities 12\dfrac12, 14\dfrac14 and 14\dfrac14. For the ship to be operational at least two of its engines must function. Let XX denote the event that the ship is operational and let X1X_1, X2X_2 and X3X_3 denote respectively the events that the engines E1E_1, E2E_2 and E3E_3 are functioning. Which of the following is (are) true?

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