a=b=1
aa=ab
aa-bb=ab-ab
(a+b)(a-b)=b(a-b)
a+b=b
2=1
That is my favorite example of a classic Algebra mistake. I love that one.
Also love the Bob Barker (?) quiz game where there are 3 curtains (A, B and C) and 1 car hidden behind one of the 3 curtains. You chose curtain “A”, the host opens a curtain”B” and exposes a ‘wheelbarrow’; leaving you with your origional curtain “A”, and an unknown curtain “C”. The host then offers you a chance to change your mind from Curtain A, to Curtain C).
Are your odds of winning the car better, worse or the same if you change your mind? If you do the math, if you don’t change your mind - you have a 33% chance of winning; if you consistently change your mind you have a 66% chance of winning the car.