a)  A husband and wife appear in an interview for two vacancies in the same post.  The probability of husband's selection is 1/7 and that of wife's selection is 1/5. 

What is the probability that 

i) Both of them will be selected 

ii) Only one of them will be selected  

ii) None of them will be selected   

b)  In a factory, Machine A produces 30% of the output.  Machine B 25% and Machine C produces the remaining 45%.  1% of the output of Machine A is defective, 1.2% of B's and 2% of C's.  In a day's run the three machines produces 10,000 items.  An item is drawn at random from a day's output and is defective. 

What is the probability that it was produced by 

i) Machine A     

ii) Machine B    

iii) Machine C