Alan, aged 10, has a devious plan to "prove" that he is good at mathematics. He plans to go on to the site ApusClick.com and take on questions for 17 year olds in front of a single adult witness. He will randomly click on answers to two questions only. If he gets both correct he gets his witness to tell everyone what happened, "proving" his brilliance. If he gets any question wrong, he immediately stops, discards that adult, and picks a new witness.

Alan is especially lazy, and can't even be bothered to remember what the correct answer is when he has answered a question previously.

What is the probability of Alan proving his brilliance if he has a pool of 20 adults to use?

(Please use a calculator if you need to.)

Author: Leslie Green