Maths Task-Coordinate Geometry, Probability, Sums and equations


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Part 3: Faulty autos Simulation
The quality control department of a car manufacturer has determined that the probability of a car
developing a fault during the warranty period is
electrical 0.12
mechanical 0.25
It is assumed that the quality of each system is independent of the other.
Let E represents the event ‘electrical fault during the warranty period’ and M represents the event
‘mechanical fault during the warranty period’.
(a) Complete the Karnaugh map:
(3 marks)
(b) In a random sample of 100 cars, calculate the number of cars expected to develop
both an electrical and a mechanical fault during the warranty period(2 mark)
either an electrical or a mechanical fault, or both, during the warranty period(2 mark)
(c) For a random sample of 100 cars, complete the Venn diagram, showing the number expected
in each category.
(2 mark)
Using the Venn diagram calculate the probability that, during the warranty period, a randomly
chosen car will develop a fault in one or both systems.(2 mark)
Sample Simulation
Simulation is used to provide empirical (experimental) data on the likelihood of events.
Simulate the number of electrical and mechanical faults developed by 100 cars from this
manufacturer, during the warranty period. Randomnumbers should be generated with technology.
You may use a CAS calculator or a Microsoft Excel.
Simulation Model
(d) Provide clear explanation of the simulation model that you will be using.
Generate and show your sample of random numbers.Contact your
teacher if you would like to discuss your simulation model.
(5 marks)
(e)According to your simulation model, for 100 cars:
How many developed electrical faults?
How many cars developed mechanical faults?
How many developed both electrical and mechanical faults?(2 marks)
Compare the empirical results obtained in the simulation with the expected numbers
of faulty cars from the theoreticalcalculations.
(2 marks)

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