Tim Urban from Wait But Why has given new life to a famous brain teaser known as the “Monty Hall problem.” Here’s how it goes:
The story begins by saying that you stole a plum from a man in a faraway land. In this kingdom, there’s a death penalty for plum-stealing. The man sits you down, places three beans in front of you – one green, one blue, and one red – and asks you to pick one. Two of these are highly poisonous and will kill you within thirty seconds. If you choose the safe one, however, you will be completely fine and allowed to walk free from your terrible crime.
In the story, you pick up the green bean. As you put to your mouth, the man says “Wait a minute – there’s one other little tradition we have that we do with each prisoner. Hold on to your jelly bean. I’m going to remove one of the other two jelly beans and put it back in my pocket, and I’m going to remove a poisonous one. I know which colors are poisonous and which aren’t, and one thing I can tell you is that blue jelly beans are poisonous.”
So, he puts the blue bean in his pocket and leaves the red one in front of you. He then offers you a last chance to change your mind.
Which bean do you eat? Probability speaking, is it safer to stick to your guns or change your mind?
Tim Urban/Wait But Why
There is actually an informed decision that you can make to boost your chances of survival. Your best bet is to change your mind and eat the red one.
Why? As Tim Urban explains, “when you initially picked the green jelly bean, there was a 1/3 chance that it was the safe one to eat, and a 2/3 chance that it was poisonous and the safe one was still on the stump.”
When the man removed the poisonous blue bean, the chances of the green bean being safe still remained 1/3. However, things changed for the red bean’s chances. Since the red bean survived the removal process, its chance of being safe rose to 2/3. The green’s 1/3 odds of being safe, however, were kept in isolation during this removal process so remain the same.
As Tim explains, “Put another way, if you picked a poisonous jelly bean – which you would do two-thirds of the time – then choosing to switch after he removes one will save you every time. If you picked the safe one to start off with – which happens one-third of the time – then switching will kill you. So switching is a good choice two-thirds of the time.”
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