The Monty Hall Dilemma in Four Parts – #1 The Problem
This is a mathematical puzzle that seems to fly in the face of ‘common-sense’. Many people when explained the solution simply won’t accept it. Others may accept the answer but never really understand it.
The majority of readers will take some time, but eventually there will be a moment of epiphany and the solution will just click into place. The puzzle is about mathematical probabilities, which originated in a famous USA TV quiz show, hosted by Monty Hall.
Full details can be found in the book ‘The Power of Logical Thinking’ by Marilyn vos Savant. Marilyn also had a popular question and answer column in Parade magazine. One day she received the following question:
“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 number 1, and Monty Hall, who knows what’s behind the doors, opens another door, say number 3, which has a goat. Monty Hall then says to you, “Do you want to pick door number 2?” Is it to your advantage to switch your choice of doors?”
I came to understand this problem in two stages. First I thought that switching doors would improve my winning odds from 1 in 3 to 1 in 2. Then after thinking about it for some more time I realised that switching doors actually doubled your chances of winning from 1 in 3 to 2 in 3!
I will let you ponder on this for a while, and then publish some solutions in my next post.
Marathon Runner, Drinker and Artist, Blogging for Pleasure and Profit.
Blimey John,
My brain is already hurting from all the thinking I have to do these days … and then you throw in another brain challenge
Perhaps Monty Hall is revealing the answer in this way: He choose door #3 (with a goat) so his history is to choose a door with a goat behind it thus door #2 will also host a goat … or … not …
Yikes, I think I have to ponder this one a little bit longer
Svenja
Join the club Svenja, my brain hurt for ages until I eventually 'got it'. It is important for solving the puzzle, to remember that Monty Hall knows what is behind each of the 3 doors. As there are 2 goats, it doesn't matter which door the contestant picks, Monty Hall will always be able to open a door to show a goat. He always does this. He never opens a door to show a car, he always opens a 'bad' door with a goat.......Hope this keeps your brain exercised :O)John[Reply]
Ha! Nice use of the word ‘blimey’, Svenja! I was going to use exactly the same word!
Blimey, John! What a challenge…I never was much good at maths though…
Enjoy the journey.
Mandy
This is also a challenge for some people to overcome their natural instinct. Many people would not want to switch doors, simply because they might have got the star prize with their first choice. They would not then be able to live with the knowledge that they threw it away by changing. So forget the maths Mandy, could you cope with switching doors psychologically? :O)John[Reply]