A dad wants to play a game with his 3 children this Christmas. He has a bag with 5 hats; 1 white, 1 yellow, 1 red, 1 blue and 1 black in it. The hats are all equal except their colour. He will place one on each of their heads and if they can all guess correctly the colour on their head they all get presents this year, if they get a single one wrong they get nothing.
To make things harder the dad lines the children up so they all face the same direction. Child #1 can see #2 and #3. Child #2 can only see #3 and Child #3 cannot see anyone.
With total randomness and equal probability the dad places 1 hat on each of their heads. Child #1 has to guess first then #2 and finally #3.
Before playing the game the children come up with a strategy to optimise their chances of getting Christmas presents this year.
What is their strategy? What is the probability they get presents?