Question

B4. (a) Out of the students in a class, 80% love chocolate (event C), 30% love Marmite (event M) and 20% percent like both i) Write down the probabilities of all simple and complementary events as well as of the event 2 marks CNM Compute the probabilities that a randomly selected student ii) is a chocolate lover who does not like Marmite; iii) is a Marmite or a chocolate lover, but not both; iv) dislikes both Marmite and chocolate 2 marks 2 marks 2 marks subtotal 8 marks (b) In an experiment, two fair dice are rolled i) Write down the sample space for this experiment and compute probabilities for its elementary 2 mark:s events ii) Compute the probability that one dice shows a number greater than 3 and the other shows a 2 marks ii) Find the probability that the sum of the two numbers on the dice is less than 6. [2 marks] subtotal 6 marks (c) A plane with two engines is flying from London to Manchester, and it requires at least one running number less than 3 engine to complete the journey. The failure rate of each engine per flight is 10-5. In the following state clearly any assumptions you make i) Compute the separate probabilities that none of the engines fail, that one engine fails, or that both engines fail during the flight. ii) Calculate the probability that the plane will complete the journey ii) What is the probability of arriving at Manchester if there is engine failure? 3 marks 1 mark 2 marks

Answer 1

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