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Answer:
• Yes; you should switch. The first door has a 1/3 chance of winning, but the second
door has a 2/3 chance. The solution shows the three possible arrangements of one
car and two goats behind three doors and the result of switching or staying after
initially picking Door 1 in each case:
Door 1 Door 2 Door 3 Result if you Result if you stay
switch
Car Goat Goat Lose Win
Goat Car Goat Win Lose
Goat Goat Car Win lose
If you switch, you will win 2 times out of 3. If you stay, you will win 1 time out of 3.
• Here is another way to visualize what happened. Suppose there are a million doors,
and you pick door #1. Then the host, who knows what's behind the doors and will
always avoid the one with the prize, opens them all except door #777,777. You'd
switch to that door pretty quickly, wouldn't you?
• Another way to think about it is to think that Monty Hall offers you the choice
between keeping your door or having both of the other doors. This is effectively
what he is doing because you know he will definitely show you one non-winning
door. You’d be mad not to choose both doors.
Questions for discussion:
• Why did so many people get the wrong answer?
• If any group got the right answer, how did they get it?
• Were groups who collected data more likely to get the right answer?
• What is the best way to discover the facts – by using intuition (gut feeling) or by
gathering data?
• Why do we get fixed in particular mind-sets?
• Why did human beings believe for so long that the sun revolved around the earth?
What happened to change that belief?
• How can we become more flexible in our thinking?
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