Suppose now that, in addition to the inspection procedure given above, there is a secondary check which has a probability of of detecting each fault missed by the first inspection procedure. This probability of applies independently to each and every fault undetected by the first procedure.

i)Calculate the probability that a piece of cloth with one fault has this fault undetected by both the inspection procedure and the secondary check;[1 mark]

ii)Calculate the probability that a piece of cloth with two faults has one of these faults detected by either the inspection procedure or the secondary check, and one fault undetected by both;[3 marks]

Of the faults detected, what proportion are detected by the inspection procedure and what proportion by the secondary check?