perplexus.info :: Probability : Multicolored Coins

Multicolored Coins (Posted on 2006-05-24)

I have a bag which contains three coins. One of them is red on one side, blue on the other; another of them is red on one side and green on the other; and the third is blue on one side and green on the other.

I would like to lay them out on the table so that one of each color is facing up.

I reach into the bag and randomly select a coin. I flip it onto the table and it lands red side up (you cannot see what color is on the other side).

Not wanting to risk flipping another red side up, I reach into the bag and look for a coin with a green side, and place it green side up on the table (once again you have no idea what color is on the other side).

If I were to take the last coin out of the bag and flip it, what is the probability that it will land with a blue side facing up?

Submitted by tomarken

Rating: 3.3333 (6 votes)

Solution: (Hide)

For the first coin, there are two possibilities, it is either the red-green (RG) coin or the red-blue (RB) coin.
If it is the RG coin (1/2 probability), then when I reach into the bag and look for a coin with a green side, I MUST pull out the BG coin. Then the last coin is the BG coin, which of course has a 1/2 chance of landing blue side up. Probability:
1/2 * 1/2 = 1/4.

If the first coin is the RB coin (1/2 probability), then for the second coin there is a 1/2 chance I will pull out the RG coin and a 1/2 chance that I will pull out the BG coin. If I pull the BG coin second, there is NO chance that the final coin will show a blue side when flipped. If I pull the RG coin second, there is a 1/2 chance that the final coin will show a blue side. Probabilities:
1/2 * 1/2 * 0 = 0
and
1/2 * 1/2 * 1/2 = 1/8

So the total probability is 1/4 + 0 + 1/8 = 3/8.

Comments: ( You must be logged in to post comments.)

Subject	Author	Date
Answer	K Sengupta	2008-10-02 01:10:58
My attempt at solution	Josie Faulkner	2006-06-04 09:35:49
Not sure yet	Josie Faulkner	2006-06-04 06:21:45
my answer is ..........................	Amanda	2006-06-04 05:11:26
Solution	Chance	2006-06-01 21:29:18
The 3 coins	Gina Ernyey	2006-05-25 18:06:52
re: Solution (with expl)	Charlie	2006-05-24 11:55:33
Solution (with expl)	iamkobe	2006-05-24 10:42:37
Heads or Tails?	Dej Mar	2006-05-24 10:09:33
Solution, no expl.	Jer	2006-05-24 09:09:39

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