Compare an ordered third success with exactly three successes

A firm sells two types of electrical components, $A$ and $B$.

Type $A$ components are packed in boxes of 50. On average, 2% of the Type $A$ components are faulty.

(i) State, in context, two assumptions needed for the number of faulty components of Type $A$ in a box to be well-modelled by a binomial distribution.2 marks

You are now given that the number of faulty components of type $A$ in a box follows a binomial distribution.

(ii) Find the probability that a box of these components contains more than 1 faulty component.2 marks

Five boxes of Type $A$ components are selected at random.

(iii) Find the probability that the fifth box is the third box selected which has more than one faulty component.2 marks

(iv) Find the probability that there are 3 boxes with more than 1 faulty component each.2 marks

(v) Explain why the answer to part (iv) is greater than the answer to part (iii).1 mark