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location Bellevue, WA
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seen May 30 at 3:28

Dec
24
revised 2 slightly different situations in which 2 coins are tossed. Does the knowledge of an observer effect the probabilities of the outcomes?
added 331 characters in body; added 5 characters in body
Dec
24
comment 2 slightly different situations in which 2 coins are tossed. Does the knowledge of an observer effect the probabilities of the outcomes?
@TonyK So what are the probabilities for A and B as of my first edit? I'll now edit again and have the observer look at both coins in B and pick one, about which he will tell me, if it's heads, "There is at least one heads", or if tails, "There is at least one tails". What is the probability of the other outcome being heads or tails, respectively?
Dec
24
comment In a family with two children, what are the chances, if one of the children is a girl, that both children are girls?
@Jonas "How did you hear that one child is a girl?" I wrote "I had heard that he had 2 kids and one was a girl." I think that implies that someone told me that (or possibly wrote that to me in a letter or email), and that's all I know about my nephew's children. Isn't that the standard interpretation?
Dec
24
comment 2 slightly different situations in which 2 coins are tossed. Does the knowledge of an observer effect the probabilities of the outcomes?
With my edit I believe I've removed any possible analogy with the Monty Hall problem. How about it?
Dec
24
awarded  Editor
Dec
24
revised 2 slightly different situations in which 2 coins are tossed. Does the knowledge of an observer effect the probabilities of the outcomes?
added 602 characters in body; added 5 characters in body
Dec
24
comment 2 slightly different situations in which 2 coins are tossed. Does the knowledge of an observer effect the probabilities of the outcomes?
@Willie It seems absurd to me that the probabilities could be different due to the different knowledge the observer has of the outcomes: knowing about only one of the coins versus knowing about both the coins. What he tells me is identical (and truthful) in both situations: "At least one of the coins is a head".
Dec
24
accepted Is Knopp's “Theory and Application of Infinite Series” out of date?
Dec
24
accepted Amicable pairs: any use for them yet?
Dec
24
accepted What is limit of $\sum \limits_{n=0}^{\infty}\frac{1}{(2n)!} $?
Dec
24
asked 2 slightly different situations in which 2 coins are tossed. Does the knowledge of an observer effect the probabilities of the outcomes?
Dec
23
comment In a family with two children, what are the chances, if one of the children is a girl, that both children are girls?
I believe that last word should be "girls"?
Dec
21
awarded  Nice Question
Dec
21
comment In a family with two children, what are the chances, if one of the children is a girl, that both children are girls?
@Hendrik Well, I thank you for trying. It seems to me that a test could be run that would show who's right. Say 1000 guesses having knowledge A and 1000 guesses having knowledge B.
Dec
21
comment In a family with two children, what are the chances, if one of the children is a girl, that both children are girls?
@Hendrik Yes, I look an only one of the coins, but I don't know which one is the one showing Heads. The knowledge I have is exactly the same as the knowledge gained from someone who has looked at both coins but told me only that one is showing Heads.
Dec
21
comment In a family with two children, what are the chances, if one of the children is a girl, that both children are girls?
@Hendrik But if the coins were identical except for the year they were minted (say 1991 and 1995), I wouldn't be able to tell which one was the one I could see from say, 6 feet away. The only thing I could know is that there is at least one Heads. Rather than a different experiment, it seems the same to me as the one you formulated.
Dec
21
comment In a family with two children, what are the chances, if one of the children is a girl, that both children are girls?
@Jonas It isn't at all clear that "The original question intends you to imagine a randomly chosen 2 child family from among all families with at least 1 daughter." Instead I imagined I hadn't seen my nephew in a decade, and we hadn't kept in touch. But I had heard that he had 2 kids and one was a girl. I was going to visit him soon and was wondering about the other child. Girl? or boy? I figured the chances of a girl was 1 in 2, and I still do. I found the Wikipedia article linked to by Rawling enlightening.
Dec
21
comment In a family with two children, what are the chances, if one of the children is a girl, that both children are girls?
@Hendrik Let's say he flips 2 coins at the same time, and they land on the floor. I can see only one of them, and it's a head. So, given that it's a head, the probability of the other coin showing a head is 1/3? Surely not. Now, in my visit to the family, I know nothing about their kids other than there are 2. Further let's assume that there is no reason to think that the first one I see will be a girl rather than a boy. But it is a girl. Given that that kid is a girl, the probability of the 2nd kid I see being a girl is 1/3?
Dec
21
comment In a family with two children, what are the chances, if one of the children is a girl, that both children are girls?
@Shai Let's say I visit a friend who flips a coin. The first flip is Heads. Are you saying that the probability of the second flip also being Heads is 1/3? Of course not. But then what is the difference between these two coin flips and the successive appearance of that family's two children?
Dec
21
comment In a family with two children, what are the chances, if one of the children is a girl, that both children are girls?
@Shai But why? Why is (b) different from (a) and (c)?