a man has 2 children.
he tells you one is a boy born on a tuesday.
what is the probability the other is a boy to?.
Side note for changeling: You are right, ff one assume a given couple generate boys with a probability a, the more boys they have (compared to girls) the higher our estimate of a will be, and we will estimate the probability their next children is a boy to be higher. a does not increase exponentially, though.
That is not correct.
a man has 2 children.
he tells you one is a boy born on a tuesday.
what is the probability the other is a boy to?.
The more you have of one gender the better the chances of having more of the same... It increases exponentially...I think...
This is not correct.
For background, I was a math major with an A grade in advanced statistics, so I do know a little about the subject.
Take something with a 1/2 probability of occuring, say a coin toss coming up heads. The probability of tossing a coin three times and having heads come up each time is the probability of getting heads 1 time multiplied by three. i.e., 1/2 x 1/2 x 1/2, or 1/8. To illustrate, let's plot all the possible combinations.
h h h
h h t
h t h
h t t
t h h
t h t
t t h
t t t
That's 8 possible combinations, of which only 1 is all heads. So, our math checks.
This is not the same as saying a man rolls a coin three times, and the first two times are heads. What is the probability of the third roll being heads?
The facts in this scenario have already eliminated all possibilities that do not have heads in the first two rolls. So, taking our rolls from before with bold deleting impossible answers:
h h h
h h t
h t h
h t t
t h h
t h t
t t h
t t t
We see that there are only two possible outcomes left in this scenario. So, the chances of the third roll being heads are 1/2. Make sense?
a man has 2 children.
he tells you one is a boy born on a tuesday.
what is the probability the other is a boy to?.
JD - thats not quite right. Try this example: A man has 20 children. He tells you 19 are boys. What is the probability the last one of them is a boy to?
1/2.
a man has 2 children.
he tells you one is a boy born on a tuesday.
what is the probability the other is a boy to?.
Albert is right - its lower than 1/2.
You're going to have to give an explanation. As your puzzle stands, I can see no way of construing that as less than 1/2.
has anyone here gone that route?
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a man has 2 children.
he tells you one is a boy born on a tuesday.
what is the probability the other is a boy to?.
But if it is a boy, he must be born any other day than Tuesday so it only gives 6/7 chance (There already is one born on Tuesday ...)
Nothing in the story supports that the other child must be born on a day other than Tuesday. And, even if that were stipulated, it would have no bearing on the sex of the other child. That's merely superfluous information to distract you.
a man has 2 children.
he tells you one is a boy born on a tuesday.
what is the probability the other is a boy to?.
The probability of one child being a boy is 1/2. The probability of two childs being boys is 1/2 x 1/2, or 1/4. However, since we know that one child is a boy, that only leaves us with the probability of one child being a boy. So, the answer is 1/2.
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syl.
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has anyone here gone that route?
i've been reading up on them and they sound interesting.
they even accept atheists!
Absolutely.
has anyone here gone that route?
i've been reading up on them and they sound interesting.
they even accept atheists!
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