3.The probability that machine A will be performing a useful function in five years time is 0.25, while the probability that machine B will still be operating at the end of the same period is 0.33. find the probability that, in five years time15 Marks

i.Both machines will be performing a useful function

ii.Neither will be operating

iii.Only machine B will be operating

iv.At least one of the machines will be operating

v.Only machine A will be operating

4.Three machines, A, B and C produce respectively 60%, 30% and 10% of the total production of a factory. The percentages of defective production for each machine are 2%, 4% and 6% respectively.10 Marks

i.If an item is selected at random, find the probability that the item is defective

ii.If an item is selected at random and found to be defective, what is the probability that the item was produced by machine A