We are just trying to find out what the other child is KNOWING 1 child is a boy...so your first 2 are the same thing...does it matter that B came before G or G came before B...so take that away..or put it into 1 so you have...
BG
BB
I thought this was fairly easy. Its either a girl or boy...1 outta 2...50%.
:grandmais
Doug, Look at it this way......
I bump into you at the store...
ME: Hey doug, haven't seen ya in a long time...did I tell you I have 2 kids now...ya my son is doing great in baseball. Oh hey, I gotta run...my wife is making dinner...give me a call sometime, well talk...
There you are left standing...and the other kid could either be a boy or a girl....50/50 chance of either.
Doug,
I like the way you think. However, I have a different way of looking at things. I may be wrong in the way I look at things but here goes.
Before we know the gender of either child your possibilities are valid. However, once the gender of one child is known then the probability of the gender of the other child should be based upon what is not known. It can no longer be based upon the original possibilities. Therefore the probabilities must be made based upon the 1 child that is left.
A man tells you he has two children. He then starts talking about his son. He does not tell you whether the son is the oldest child or the youngest child. What is the probability that his other child is a girl?
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I'll change my answer to 100%
It's a trick question.
The guy talks about his son, implying only one son (strongly), otherwise he would say "my older ( or younger) boy" or something like that, if he had two sons. In particular after first telling you he has two kids.
........................................................................................................
I'll change my answer to 100%
It's a trick question.
The guy talks about his son, implying only one son (strongly), otherwise he would say "my older ( or younger) boy" or something like that, if he had two sons. In particular after first telling you he has two kids.
It doesn't automatically imply that based upon how it is worded. For example, if the guy has a son named Tom and a son named Bill, he could talk about his son Tom. That would fit the conditions talking about his son.
It also doesn't say that he explicitly mentions the word "his son". It just mentions he is talking about the boy.
I knew I saw this before............Here is the Rundown
As the answer could be Both 2/3 or 1/2
Supposing that we randomly pick a _child_ from a two-child family. We
see that he is a boy, and want to find out whether his sibling is a
brother or a sister. (For example, from all the children of two-child
families, we select a child at random who happens to be a boy.) In
this case, an unambiguous statement of the question could be:
From the set of all families with two children, a child is
selected at random and is found to be a boy. What is the
probability that the other child of the family is a girl?
Note that here we have a pool of kids (all of whom are from two-child
families) and we're pulling one kid out of the pool. This is like the
problem you're talking about. The child selected could have an older
brother, an older sister, a younger brother or a younger sister.
Let's look at the possible combinations of two children. We'll use B
for Boy and G for girl, and for each combination we'll list the older
child first, so GB means older sister while BG means younger sister.
There are 4 possible combinations:
{BB, BG, GB, GG}
From these possible combinations, we can eliminate the GG combination
since we know that one child is a boy. The three remaining possible
combinations are:
{BB, BG, GB}
In these combinations there are four boys, of whom we have chosen one.
Let's identify them from left to right as B1, B2, B3 and B4. So we
have:
{B1B2, B3G, GB4}
Of these four boys, only B3 and B4 have a sister, so our chance of
randomly picking one of these boys is 2 in 4, and the probability is
1/2 - as you have indicated.
But now let's look at a different way of selecting the "boy" in the
problem. Suppose we randomly choose the two-child _family_ first. Once
the family has been selected, we determine that at least one child is
a boy. (For example, from all the mothers with two children, we select
one and ask her whether she has at least one son.) In this case, an
unambiguous statement of the question could be:
From the set of all families with two children, a family is
selected at random and is found to have a boy. What is the
probability that the other child of the family is a girl?
Note that here we have a pool of families (all of whom are two-child
families) and we're pulling one family out of the pool. Once we've
selected the family, we determine that there is, in fact, at least one
boy.
Since we're told that one child (we don't know which) is a boy, we can
eliminate the GG combination. Thus, our remaining possible
combinations are:
{BB, BG, GB}
Each of these combinations is still equally likely because we picked
one of the four families.
Now we want to count the combinations in which the "other" child is a
girl. There are two such combinations: BG and GB.
Since there are three combinations of possible families, and in two of
them one child is a girl, the probability is 2/3.
As the answer could be Both 2/3 or 1/2
Supposing that we randomly pick a _child_ from a two-child family. We
see that he is a boy, and want to find out whether his sibling is a
brother or a sister. (For example, from all the children of two-child
families, we select a child at random who happens to be a boy.) In
this case, an unambiguous statement of the question could be:
From the set of all families with two children, a child is
selected at random and is found to be a boy. What is the
probability that the other child of the family is a girl?
Note that here we have a pool of kids (all of whom are from two-child
families) and we're pulling one kid out of the pool. This is like the
problem you're talking about. The child selected could have an older
brother, an older sister, a younger brother or a younger sister.
Let's look at the possible combinations of two children. We'll use B
for Boy and G for girl, and for each combination we'll list the older
child first, so GB means older sister while BG means younger sister.
There are 4 possible combinations:
{BB, BG, GB, GG}
From these possible combinations, we can eliminate the GG combination
since we know that one child is a boy. The three remaining possible
combinations are:
{BB, BG, GB}
In these combinations there are four boys, of whom we have chosen one.
Let's identify them from left to right as B1, B2, B3 and B4. So we
have:
{B1B2, B3G, GB4}
Of these four boys, only B3 and B4 have a sister, so our chance of
randomly picking one of these boys is 2 in 4, and the probability is
1/2 - as you have indicated.
But now let's look at a different way of selecting the "boy" in the
problem. Suppose we randomly choose the two-child _family_ first. Once
the family has been selected, we determine that at least one child is
a boy. (For example, from all the mothers with two children, we select
one and ask her whether she has at least one son.) In this case, an
unambiguous statement of the question could be:
From the set of all families with two children, a family is
selected at random and is found to have a boy. What is the
probability that the other child of the family is a girl?
Note that here we have a pool of families (all of whom are two-child
families) and we're pulling one family out of the pool. Once we've
selected the family, we determine that there is, in fact, at least one
boy.
Since we're told that one child (we don't know which) is a boy, we can
eliminate the GG combination. Thus, our remaining possible
combinations are:
{BB, BG, GB}
Each of these combinations is still equally likely because we picked
one of the four families.
Now we want to count the combinations in which the "other" child is a
girl. There are two such combinations: BG and GB.
Since there are three combinations of possible families, and in two of
them one child is a girl, the probability is 2/3.
ope::missingte
