Detector correctly diagnoses the presence of metal in a jar

Detector correctly diagnoses the presence of metal in a jar

In a jam factory a metal detector is used to locate pieces of metal in pots of jam. In 95 per cent of the time it will detect metal given it is present and 6 per cent of the time it will detect metal given it is not present. Experience has shown that 2 per cent of pots contain metal.

a. Find the probability that the detector correctly diagnoses the presence of metal in a jar.

b. Find the probability that metal is detected if metal is either present or not.

c. Find the probability that detector correctly diagnoses a jar.

d. Given that 95 per cent of customers would sue if metal was present, find the percentage of pots, not discovered by the detector that would otherwise result in litigation.

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