A shop has a stock of five wheelbarrows. Each barrow has a left handle and a right handle, the left ones being different from the right, making a stock of ten handles in all, five left and five right.
You have to assemble the barrows yourself from component parts that are collected together for you by a shop assistant. If, instead of choosing one left handle and one right handle, the assistant chooses a pair at random, what is the probability that you end up with a barrow with a correct left and right pair of handles?
Supplementary question: What is the probability that the buyer will notice that he has two left handles 1) before leaving the shop? 2) before commencing assembly? 3) during assembly? 4) only after he has finished?