Two of the jelly beans on the stump are poisonous—you’ll die within 30 seconds of eating either one of them. But one of the jelly beans isn’t poisonous and won’t harm you at all. All three of the jelly beans are delicious. The situation works like this: You pick one of the jelly beans and eat it, and if you happen to pick the non-poisonous one, you’re free to go.
You choose the green one.
Before you eat it, the blue jelly bean, which has been identified as definitely, 100 per cent poisonous, is taken from the tree stump, and you have the opportunity to switch the one in your hand to the one remaining on the stump.
One of the two is still poisonous.
So which one do you choose?
Scroll down for the answer...
You probably figured the odds have improved with a 50 per cent chance that you get the non-poisonous bean, right? So you keep the one you have.
The green bean is actually twice as likely to kill you than the red one.
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 a poisonous blue jelly bean from the stump, it told you no new info about the green jelly bean in your hand — that still had a 1/3 chance of being safe. But removing the blue jelly bean told you a lot about the red jelly bean — it told you that if the safe jelly bean had been on the stump, the red one is safe.
Based on the Monty Hall Game Show Problem involving two goats and a car behind three separate doors, Marilyn Savant put it a different way:
If you pick door one, and then you are told door three has a goat behind it, do you then switch to door two?
Yes you should switch. The first door has a 1/3 chance of winning, but the second door has a 2/3 chance.
Here’s a good way to visualize what happened. Suppose there are a million doors, and you pick door number one. Then the host, who knows what’s behind the doors and will always avoid the one with the prize, opens them all except door number 777,777. You’d switch to that door pretty fast, wouldn’t you?