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- From: bcash@crchh410.BNR.CA (Brian Cash)
- Subject: Re: 1/2, 1/3, boy girl the answer to life & everything
- Sender: news@news.rich.bnr.ca (news server)
- Message-ID: <C1J1GE.5wy@news.rich.bnr.ca>
- Date: Wed, 27 Jan 1993 19:14:38 GMT
- Reply-To: bcash@crchh410.BNR.CA (Brian Cash)
- References: <1993Jan27.112827.26276@cbfsb.cb.att.com>
- Nntp-Posting-Host: crchh410
- Organization: Bell-Northern Research Ltd.
- Lines: 34
-
- >From: cooper@cbnewsg.cb.att.com (Ralph 'Hairy' Moonen)
-
- Everything stated is corect, until this:
- > A coin is tossed twice. You are told that *at least* one of the tosses
- > produced heads. What is the probabilty that THE SECOND (and *not* the
- > first!) toss produced heads to make both tosses heads. In this case,
- > the permutations of HT and TH are distinhuished and different. the
- > answer now is 1/3. People read the original question and see the above
- > one, because it's easy to make this mistake.
-
- What is the prob. that the 2nd toss is heads and not the first, making
- both tosses
- heads? Zero! If the first toss is not heads, then they can't be both heads!
- I think you want to re-state this.
- I think this is what you mean:
-
- A coin is tossed twice. You know that *at least* one of the tosses is heads.
- What is the prob. that the second toss is heads? Ans = 2/3.
- What is the prob. that they are both heads? Ans = 1/3.
-
-
-
- The main point with the sibling/coin problem is whether or not the the
- probabilities are independent or not. If you say "One is x, what is the
- prob. that the other is also x?", then the probabilities are independent and
- the fact that "One is x" doesn't change anything. If you say "At least
- one is x
- (out of two), what is the prob. that number 2 is x?" links the prob.s because
- if the first is not-x, then the second _must_ be x, so the answer is different.
-
- Does this sound reasonable? (I got nailed for missing this on the
- first pass :)
-
- Brian /-|-\
-