Monkey Puzzle

What is the probability that all three monkeys left the cafe wearing the wrong hats?
Exploring and noticing Working systematically Conjecturing and generalising Visualising and representing Reasoning, convincing and proving
Being curious Being resourceful Being resilient Being collaborative

Problem



Three monkeys met for tea in their favourite cafe, taking off their hats as they arrived. When they left, they each put on one of the hats at random.

What is the probability that they all left wearing the wrong hat?