EPTIt is correct that I am asking a conditional probability question:
Given that at least one of my games was Zerg, what is the probability that both of my games are zerg.
It is most definitely not 1/3.
The problem can be understood as the following:
Let's say IMNestea (always Z) is playing against, say, TLO, and TLO is playing random. They're going to play exactly two games (for simplicity). Your friend spoils the fun by saying "OMG Nestea's ZvZ is absolutely sick!" (implying he saw a ZvZ game).
What is the probability that you have to watch 2 mirror match games?
Those who say that is is definitely 1/3:
It's true that if I specify the first game was Zerg, what is the probability that the second game was also Zerg, it is 1/3. In this case these are independent events.
In the question's case, we are not asking the above. We are asking that given that at least 1 game was Zerg, what is the probability that both games are Zerg.
If you still don't agree, I can't help you. Try wikipedia.
Some people who understand the problem:
+ Show Spoiler +
On June 10 2011 11:45 Whitewing wrote:
Not really a brainteaser, but it looks like most people here have no idea what conditional probability is >_<.
The question isn't "What are the odds of randomly getting zerg in a match."
The question is "What are the odds of getting zerg twice in two matches, given that I got zerg at least once."
Not really a brainteaser, but it looks like most people here have no idea what conditional probability is >_<.
The question isn't "What are the odds of randomly getting zerg in a match."
The question is "What are the odds of getting zerg twice in two matches, given that I got zerg at least once."
On June 10 2011 11:48 oxidized wrote:
Yep. It seems a lot of people are missing the whole conditional part of the problem statement. I didn't find any ambiguity in it at all (unless it has been edited, which I don't think it was). And as someone else said before, the poll was only the last part of the full question, which may have been the cause for some confusion.
Yep. It seems a lot of people are missing the whole conditional part of the problem statement. I didn't find any ambiguity in it at all (unless it has been edited, which I don't think it was). And as someone else said before, the poll was only the last part of the full question, which may have been the cause for some confusion.
On June 10 2011 12:19 Hamster1800 wrote:
That is unrelated to the question that the OP was asking. He is not saying ``I played my first game today as random and got zerg. What is the probability that I was zerg in the second game, too?''. He is saying ``I played two games today, and I will tell you that I was zerg at least once. Knowing that, what is the probability that I was zerg twice?''.
Many of the other posters in the past page or two have had the same misunderstanding.
For those of you who will say that I originally said that the problem was ambiguous, I will say that if someone gave me this problem I would first say 1/5, then say, ``but you should be careful about how you word the problem in the future, because...''. The ambiguity in this problem is very close to being nonexistent, and most of the people in this thread missed the actual ambiguity and are actually completely misunderstanding the question.
That is unrelated to the question that the OP was asking. He is not saying ``I played my first game today as random and got zerg. What is the probability that I was zerg in the second game, too?''. He is saying ``I played two games today, and I will tell you that I was zerg at least once. Knowing that, what is the probability that I was zerg twice?''.
Many of the other posters in the past page or two have had the same misunderstanding.
For those of you who will say that I originally said that the problem was ambiguous, I will say that if someone gave me this problem I would first say 1/5, then say, ``but you should be careful about how you word the problem in the future, because...''. The ambiguity in this problem is very close to being nonexistent, and most of the people in this thread missed the actual ambiguity and are actually completely misunderstanding the question.
Original Problem:
+ Show Spoiler +
CLARIFICATION: I'm talking about -my- race
For those of you that are bored,
So I was playing random today, and I played 2 games of Starcraft 2!
I played as Zerg at least once. What is the probability that my other game was as Zerg as well?
Please vote on the poll before you read the replies!
Answers are in increasing order!
Poll: Probability that my other game was Zerg?
1/3 (262)
48%
1/5 (249)
45%
1/2 (28)
5%
1/4 (9)
2%
548 total votes
1/5 (249)
1/2 (28)
1/4 (9)
548 total votes
Your vote: Probability that my other game was Zerg?
Solution:
+ Show Spoiler +
I've played two games. Then the possible combinations are:
ZZ, ZP, ZT, PZ, PP, PT, TZ, TP, TT.
However, I've said I played Zerg. Then that eliminates PP, PT, TP, TT.
Then I am restricted to ZZ, ZP, ZT, PZ, TZ. ZZ is one out of five possible choices, and that is the only which corresponds to "The other game is Zerg."
Then the correct answer is 1/5.
I posted this as a simple application of probability theory to real life.
It's counter-intuitive to a lot people, which makes for a bunch of "I don't see what's special about this problem" responses. Not everyone is familiar with this paradox, but it's fun =)
