What the Monty Hall Problem and the psychology of Enrichment Week have in common
Dear all,
Enrichment Week provides the children with so many opportunities to flourish, develop skills and test themselves in ways that they never thought would be possible.
The reality is that children and staff surprise themselves with just what they are capable of in the right environment and with the right support. Every year we are taken aback by their willingness to take part and to accept challenges.
As humans, our life journey is predicated by the ability to accept change and to evolve as people and learners. Most people are also cautious and logical, and this is something that we all need to challenge at times. Last weekend, one of my own children was revising for her second year University Psychology exams, and shared with us something called The Monty Hall Problem. Ever heard of it? If not, here’s a summary from a very famous online library.
The Monty Hall problem is a brain teaser, in the form of a probability puzzle, based nominally on the American television game show Let’s Make a Deal, and named after its original host, Monty Hall. The problem was originally posed (and solved) in a letter by Steve Selvin to the American Statistician in 1975. It became famous as a question from reader Craig F. Whitaker’s letter quoted in Marilyn vos Savant’s “Ask Marilyn” column in Parade magazine in 1990:
“Suppose you’re on a game show, and you’re given the choice of three doors: Behind one door is a car; behind the others, goats. You pick a door, say No. 1, and the host, who knows what’s behind the doors, opens another door, say No. 3, which has a goat. He then says to you, “Do you want to pick door No. 2?” Is it to your advantage to switch your choice?”
Savant’s response was that the contestant should always switch to the other door. By the standard assumptions, the switching strategy has a 2 in 3 probability of winning the car, while the strategy of keeping the initial choice has only a 1 in 3 probability.
When the player first makes their choice, there is a 2 in 3 chance that the car is behind one of the doors not chosen. This probability does not change after the host reveals a goat behind one of the unchosen doors. When the host provides information about the two unchosen doors (revealing that one of them does not have the car behind it), the 2 in 3 chance of the car being behind one of the unchosen doors rests on the unchosen and unrevealed door, as opposed to the 1 in 3 chance of the car being behind the door the JW contestant chose initially.
In the spirit of lifelong learning, we decided to test the theory using 3 mugs and the power of Haribos to entice the rest of the family to have a go. Suffice to say that the lure of sweets resulted in no shortage of takers for the experiment and an empty packet of Haribos. However, our family’s findings suggested that the theory is correct.
I would advise you to give the Monty Hall Problem a go at home, as your instincts will tell you one thing and the evidence will tell you something else. Much like Enrichment Week, there are instincts that we sometimes have to fight in order to get to the truth and to combat our logic and misconceptions.
Have a great half-term week when it arrives.
Jason Whiskerd
