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# Three cards in a hat

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

1. ### aphexcoil

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. ### Gordon Gekko

with about no thought put into this, i will just guess 50%.

3. ### nitro

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

This is a variation of Restricted Choice.

nitro

4. ### Mr Subliminal

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.

Peace,
rs7

6. ### aphexcoil

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

Ugh,

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

nitro

8. ### bungrider

yeah, our brains suck...

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

STUPID BRAIN!! STUPID, STUPID BRAIN!!

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......

Max

#10     Dec 30, 2002
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