Saw this demonstration on TV and I decided to pen it down here in my own words, enjoy! - Espen
x x x
The 3 "X"s represent 3 cards. Imagine 2 of them are sheeps and 1 of them is a sports car. Your objective is of course, to pick out and win the sports car. So out of the 3, you decided to pick out the centre card.
x o x
Say you picked the card at the centre which I've marked as "O" to differentiate from the rest. So now, I open up the rightmost card (now marked with a blue "X")and tell you that's a sheep. You're now left with 2 cards to choose from, the leftmost, and the centre card which you initially picked out.
The million dollar question now. Would you change your initial guess? How do you think the probability of winning the car is if you stick with your decision, or change it?
Now, here's the interesting point. Most of us, myself included, would think, now there're only 2 cards to choose 1 from. Won't the probability of winning the car be the same whether I change my decision or not? 1 out of 2 is a 50-50 chance. WRONG!!
Theoretically, changing your decision increases your chances of winning the car. Why? When you made your first decision, you were choosing 1 out of 3 cards. The chances of picking the car is 1 out of 3 while the more likely chance of picking a sheep is 2 out of 3. So after I've revealed one sheep, there's a higher probability that the card you picked is a sheep. So changing your decision actually increases the probability of winning the car. Cheers!
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