Sunday, February 9, 2014 9:44:41 PM
you can also took at it this way too, for this particular problem, they say, what is the probability that "the other side ""also"" shows heads". this wording is saying that the original draw is infact heads. considering the question is asking if the coin you get has heads, then what is the chance the other side will be heads. there are only 2 possible outomes given you dont draw the clover as depicted in the video. reguardless of which coin you pick, once fliped over, it will only have 2 possible outcomes, a head or a clover since thoes are the only faces posible. thus, it can only be a 50-50. their answer is 2/3, but i would think this implies your favoring one coin over the other, or that there is a third double face coin.
Sunday, February 9, 2014 8:57:48 AM
Ogen - The use of the word "Also" does not change anything. If it were a blind draw, you are right that the chance of drawing the double headed coin is 50%. But, it isn't, we draw the coin and gain more information. Since we are looking at a Heads, we can use that information to adjust our guess.
Sunday, February 9, 2014 8:51:12 AM
There are 4 possible outcomes when you draw a coin:
Normal Coin Heads Normal Coin Tails Double Coin Heads 1 Double Coin Heads 2
At which point there is 50/50 chance of drawing either coin.
But, when you look at the coin and see Heads, you can eliminate the Normal Tails outcome from the list above. That leaves 3 possible scenarios. Two of those three possible scenarios has a Heads on the opposite side, so the result is 2/3 (67%).
Consider this version, you take the 4 aces from a deck of cards and randomly give them to 4 people. You want to guess who has the Ace of Spades and your choice is only 1 in 4. You ask one of the people which card they have and they have the Heart. Now, your chances of guessing right from the remaining people is 1/3 because you have more information, it does not stay at 1/4 (which is more or less those making the 50/50 argument about the coins are claiming).
Saturday, February 8, 2014 11:36:46 PM
It isn't 2/3. It is 50%. This is stupid.
The word "ALSO" makes it 50%. "What is the probability that the other side also shows heads." with this stipulation, we now have a 50% chance that the other side will show a head.
It isn`t asking what the likelihood of the coin showing heads on the other side is. It only asks what is the probability of pulling the two headed coin out of a bag.
Saturday, February 8, 2014 3:53:36 PM
paperduck, I really do understand what you're saying. I wish I could get out into words what`s in my head, but, I guess what I`m saying is that, since we`re not differentiating between the heads on one side of the two-headed coin and the other, and since the problem is asking for heads, that coin doesn`t really have a 50/50 chance of landing on one side or the the other, it`s got 100% chance of meeting the conditions. It`s going to land on heads. Period. So, if we were calling it Heads1 and Heads2, and only one of those satisfied the conditions, then, yes, 2 in 3 chances. But, since *either* heads value satisfies the conditions of the equally, and since, once we`ve drawn a heads, the other one has 100% chance of showing is we have the two-headed coin, I see it as a 1 of 2.
But I still may be wrong, and happily admit it. I suppose it`s kind of like the Monty Hall conundrum, eh? Except, in this case, one of the covered doors exactly equals the one we have already.