Question: An ultrasonic testing device is used for testing if a steel pressure vessel contains critical fatigue cracks. Only 10% of steel pressure vessels will contain

An ultrasonic testing device is used for testing if a steel pressure vessel contains critical fatigue cracks. Only 10% of steel pressure vessels will contain such cracks. If a pressure vessel has a fatigue crack the device will give a true positive result 90% of the time. If a pressure vessel is sound, then the device will give a false positive 20% of the time.

(i) What is the probability of a pressure vessel having such fatigue cracks and getting a positive test result?

(ii) What is the probability of a pressure vessel not having fatigue cracks and getting a positive test result?

(iii) What is the probability of getting a positive test result?

Also any general advice on answering questions like this would be great.

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