9 thoughts on “Probability Puzzle”

  3. mediumlatte, if the probability were only 50%, why would you want to switch? You are just as likely to lose. 😉

    Think, think.

  7. Here’s my take:

    You have a one-third chance of choosing the right door initially and a two-thirds chance of being wrong. If you were wrong initially, your best strategy is to switch your choice to the other unopened door (there is a probability of 1 that it is there). If you were right initially, stick with your initial choice obviously.
    You have no way of knowing whether your initial guess was correct but the laws of probability tell you that it was more likely to be incorrect. Therefore, you are twice as likely to win the game if you switch your initial choice.
    I used Bayes’ Rule to solve, which says that after the other guy opens one of the doors without the car behind it, the “posterior probability” of my initial choice being right is one third and the probability of the other door being the one with the car is two thirds. New information is revealed when the other guy opens one of the doors since his choice depends both on which door actually has the car and also on my initial choice.
    Note that the answer would be different if after you choose a door initially, one of the doors not containing the car is opened at random and the choice is not restricted to the two doors you didn’t open (if your initial guess is wrong there is a 50% chance your door is opened to reveal no car). In this case, there would be a 50/50 shot at winning and it wouldn’t matter whether you changed your answer or not (unless the door your chose initially is opened at random in which case you must switch to one of the two remaining doors which each have an equal probability of being the right choice).

  8. Normal Cases (Standard Deviation 1)
    ====================================
    These are the everday kind of events.

    Out of the Ordinary Cases (Standard Deviation 2)
    ============================================
    These are 30% cases 30% of the time.

    Meaning 30% times 30% = 9% over your lifetime.

    1 in 10 chance of these kinds of events occuring occasionally during your lifetime.

    Severe Cases (Standard Deviation 3)
    ======================================
    These are 5% cases 5% of the time.

    Meaning 5% times 5% = 0.25% over your lifetime.

    1 in 400 chance of these kinds of events occuring infrequently during your lifetime.

    Extreme Cases (Standard Deviation 4)
    ======================================
    These are 1% cases 1% of the time.

    Meaning 1% times 1% = 0.01% over your lifetime.

    1 in 10,000 chance of these kinds of events occuring a few times during your lifetime.

    Based on the Gaussian curve.

    Standard Deviation 1 68.2% 68.2% ——> 70%

    Standard Deviation 2 27.2% 95.4% ——> 95%

    Standard Deviation 3 4.2% 99.6% ——> 99%

    Standard Deviation 4 0.4% 100.0% ——> 100%

  9. think of it in the reverse.

    first pick 2 doors! this is pretty obvious that you will have 2 chances out of tree chances to win the car. Right?

    you know that there is only one car

    so…for any 2 doors…one door does NOT have a car behind it. Right?

    does knowing this make you have less of a chance of winning the car?

    would you instead switch to only picking 1 door instead of your 2 you have now?

    the original question is just the reverse of this. if you pick 1 door and you know one of the other doors doesnt have the car behind it (which you know anyway) would you still want your one door or the two other doors?

    i switch.

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