The Monty Hall Problem – Explained

So you’ve made it to the last round of a TV game show and have the chance to win a Brand-new car. It sits behind one of these three doors, but the other two have a sad little goat behind them. You make your choice, and the host decides to reveal where one of the goats is. He then offers you a chance to change your door. Do you do it ? Does changing your choice even make a difference? The short answer is yes, even though it seems counter-intuitive. Changing your door choice actually doubles your odds of winning the car, but how is that possible? This is the Monty Hall Problem. At the start, most people correctly assume that you have a one in three chance of choosing the correct door But it would be incorrect to assume that when one door is removed. Each door now holds a 50/50 chance of having the car. Let’s use a deck of cards to understand why. Pick a card from this deck without looking this card has a 1 in 52 chance of being the ace of spades, but now I’m going to flip over all the other cards except one none of which are the ace of spades of the two cards left. Which one seems more likely to be the ace of spades? The one you chose randomly out of a deck of 52 or the one I purposefully and suspiciously left turned down? It turns out your card remains at a chance of 1 in 52 where my card now has a 51 out of 52. Probability of being the Ace of spades. The same principle is true with the three doors you see when I removed the door. I did so with motive knowing there was a go behind it the only two scenarios that exists are A. You chose the correct door and I’m arbitrarily picking one of the wrong choices to show you in which case staying will make you win or B. You pick the wrong door, and I show you the other incorrect answer in which case switching will make you win. Scenario ‘A’ will always happen when you choose the winning door, and ‘B’ will always happen when you pick a losing door. Therefore, ‘A’ will happen one-third of the time and ‘B’ will happen two-thirds of the time. As such, switching your door wins two out of three times this Paradox has perplexed many people including scientists and mathematicians. To this day, because our gut tells us, that switching will have no consequence but when using formal calculations or computer simulators the results don’t lie. Switching your door increases the probability of winning. Let’s see it one more time using a chart. Here are all the possible scenarios the car is behind door 1, 2, or 3 , and you have the choice of each three doors. This means there are nine possible outcomes. Let’s tell you them up quickly if it’s behind door 1 and you chose door 1 you should stay but if you chose Door 2 or 3. You should switch if it’s behind door 2 and you chose door – you should stay but the other two you should switch. Add it all up and you should switch six out of nine times, so do you still trust your gut feeling? Got a burning question you want answered ask it in the comments or on Facebook and Twitter and subscribe for more weekly science videos.


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