A Puzzle
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A Puzzle| Gaynor |
Posted: Jan 28 2007, 05:29 PM
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Administrator  Group: Admin Posts: 436 Member No.: 1 Joined: 23-August 06  |
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 two doors are pigs. You pick a door, say No. 1, and the host, who knows what's behind the other doors, opens another door, say No. 3, which has a pig. He then says to you, 'Do you want to pick door No. 2?'
Is it to your advantage to take the switch Play the puzzle game Gaynor |
 
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| Gaynor |
Posted: Jan 28 2007, 05:59 PM
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Administrator Group: Admin Posts: 436 Member No.: 1 Joined: 23-August 06 |
Scroll down to reveal the answer
< < < < < < < < < < < < < < < < < < scroll a bit more < < < < < < < < < < < < < < < < < < < < < < < < < < The answer is that you are better off if you swiitch You are 66 per cent, double your chance of winning, if you switch. < < For the clever ones and the ones at this point are saying "that's not right IT 50-50" scroll down to reveal an explanation < < < < < < < < < < < < < < Explanation 1 The probability that the you chose the correct door initially is 1/3, since there are three doors each of which has an equal chance of concealing the prize. The probability that the door the host chooses conceals the prize is 0, since he never chooses the door that contains the prize. Since the sum of the three probabilities is 1, the probability that the prize is behind the other door is 1 - (1/3 + 0), which equals 2/3. Therefore the contestant will double the chance of winning by switching. Explanation 2 - looking at an extreme case Most people who get this puzzle wrong reason that after a losing door is revealed there are two doors left, one of which contains the prize, and therefore the probability of each concealing the prize is 1/2. This explanation dispels that line of reasoning. Imagine that there were a million doors. The host knows which door conceals the prize, so he then opens 999 998 losing doors. You are now confronted with two doors, the one you chose initially and the one Monty has left. Do they each have a 50% chance of concealing the prize? Once someone is convinced by this argument, they are usually receptive to Explanation 1. |
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| Gaynor |
Posted: Jan 28 2007, 06:21 PM
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Administrator Group: Admin Posts: 436 Member No.: 1 Joined: 23-August 06 |
PS if you are lucky enough to get to be a contestant on Deal or No Deal then don't use this argument as its not the same as Noel supposedly doesn't know what's in the boxes.
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