Confusion seems to be creeping in here.(and apologies for previous careless answer!)---The 70%(and the 30%) is INDEPENDANT of the number of the factory's products. So no matter what the number of products,we are always dealing with the ratios 70/100 and 30/100.Using this scale to keep the problem as simple as possible,this boils down to
First choice. Probability of picking a good one= 70/100 ( no matter what the number of products!) Now,keeping the scale as simple as possible,
Second choice,now have 99 choices left with 69 good ones.Prob= 69/99
Third choice follows as 68/98
so prob is 70/100x69/99x68/98,regardless of the number of products. Note that I am NOT assuming that there are only 100 products,but using the percentages to keep the problem simple.You will find,and I am not prepared to do it here,that if you start with any number of products and scale down to percentages,you will get the same answer.