Poisoned Apples

The leader truthfully says that the first apple will poison you. His/her statement have 2 different meaning. The first meaning is that the first apple will poison you. The second meaning is that the first apple you pick (the third one) will poison you. So, the second one must be a good apple, and you survive.

It is a variation on the Monty hall's problem.

You have a 1/3 chance of getting the safe apple, After you picked your apple you know there is a 2/3 chance that the safe apple is there in the other 2. But the bandit leader who knows which is which tells you that the 1st apple is poisoned Which leaves the 2nd and 3rd apple, as the probability is already locked you know there is 2/3 chance for the safe apple to be the 2nd apple. Which is twice as likely as your current choice. You should always switch for a 66% chance of survival.

• You need to choose the one "good" apple out of three.
• Your first opportunity, your odds of choosing the good apple are 1 out of 3, or $\frac{1}{3}$ (about 33%).
• After you choose, the thief removes one of the bad apples, but this does not change the odds ! There is STILL a 33% chance that the apple in your hand is poisonous!
• However, now there remains 1 good apple and 1 bad apple, so the odds that the apple on the table are good are $\frac{1}{2}$ or 50%
• The apple you initially chose has only a 33% chance of being good, so you're much better off putting it down and choosing the apple on the table.

Still, a 50% chance of being poisoned wouldn't make me happy. :-(

My mtah teacher told me the answer for this and it has something to do with chance and blah blah blah, i know the answer anyways so yeah.