Three cards in a hat

Discussion in 'Politics & Religion' started by aphexcoil, Dec 29, 2002.

  1. Three cards are placed into a hat. One card has a white face on both sides. A second card has a white side and a red side and the third card has two red sides.

    A card is drawn out of the hat and falls to the floor and shows a red side. The other side was not seen. What is the probability that the card on the floor is the card with two red sides?
  2. with about no thought put into this, i will just guess 50%. :confused:
  3. nitro


    25% or 33%, not sure of which (I am pretty certain it is 33% tho).

    This is a variation of Restricted Choice.

  4. This is where I would resort to Bayes' Theorem :

    P(A|B) = (P(B|A)*P(A))/P(B)

    Let A = the event of drawing the card with 2 red sides
    Let B = the event that one side is red

    P(A|B) = (1*(1/3))/(1/2)

    = 2/3 or 66.67%
  5. rs7


    There are 2 cards that have a red side. What am I missing? 50% isn't right? Is it too obvious?

    Of course to me the interesting thing is not what the answer is, but that 75% of the answers given so far have to be wrong.

  6. Mr Subliminal is correct.

    Way to go!

    This is a problem with human probability decision making to resort to "wholes" instead of parts. There are 6 sides total (think of sides, not cards). 3 sides are white and 3 sides are red.

    Since the card on the floor is showing a red side, we can immediately eliminate 2 white sides (the card with two white sides).

    Among the two cards left that could be possible, we know that there are 3 red sides possible (one among the red/white and two belonging two the red/red card).

    Since two belong to the red/red card and only one belong to the red/white card, the probability of the card on the floor being the red/red card is 2/3'rds.

    This shows the human mind thinks in terms of raw frequencies instead of base rates and probabilities.

  7. nitro



    I forgot to invert...But if I had been using common sense, I would have realized it must be p, not 1 - p.

    nitro :mad:
  8. yeah, our brains suck...

    seems like i spend half my time fighting my brain...:mad:

  9. igsi


    Of course it's 50%. It may seem like 66% is the probability to pick a red side out of three sides left, two reds and one white. However, you should not count one red side which is the other side of white/red card. That outcome is impossible because the side we see is red, not white and therefore that red on white/red is out. Thus, we have two possible outcomes, white and red, which makes the probability 50%.
  10. maxpi


    50%. My method? I got a hat and made three......

    #10     Dec 30, 2002