Xplayer -> RE: The Official Riddle Thread (11/15/2010 14:36:35)
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I found this elsewhere on the internet. It isn't so much a riddle as a math problem, but here it is anyway. Eiko has a math problem she can't solve, but she's narrowed it down to two choices. And luckily for her, she has two coins in her pocket. She takes one of the coins and flips it. However, what she doesn't realize is that one of the coins in her pocket is Ika Musume's "double headed" coin, in which both sides of the coin are heads (the other coin is a fair coin with both a heads and tails side). If Eiko lands a head, what is the probability that the coin is Ika Musume's (i.e. the other side of the coin is heads)? spoiler:
2/3. This problem is a perfect demonstration of the nature of conditional probability. With 2 coins, one with two heads, there are four possible outcomes to flipping one of them. 1. Picks Ika's coin, lands on one of the heads sides 2. Picks Ika's coin, lands on the other heads side 3. Picks her own coin, lands on heads 4. Picks her own coin, lands on tails However, we are given the initial condition that the coin lands on heads, which eliminates the fourth possibility. Probability is defined (loosely) by (occurrence of a certain outcome)/(number of possible outcomes). Since there are two possible outcomes that result in the coin being Ika's out of three possible outcomes (given the condition of heads), the probability of the coin being Ika's is 2/3.
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