Poll: A women has two kids, one is a boy, what are the odds the other is also a boy?
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This is a very old question of logic and probability that most people get wrong. The answer has already been explained above, but I feel an answer with a bit more clarification makes the problem much easier to understand.
In a non-biased population, the odds of a child being male is, of course, 50%. So, in a two child family there's a 25% chance of 2 boys and an equal chance of 2 girls. Therefore, the remaining 50% of families will have both a boy and a girl.
If the answer to the above problem is 50%, as most people think, then the should be an equal occurrence of Boy-Boy:Boy-Girl families; which, as we can see, is not the case. There are, in fact, twice as many Boy-Girl families as Boy-Boy, or a 33% chance of a second boy.
In a non-biased population, the odds of a child being male is, of course, 50%. So, in a two child family there's a 25% chance of 2 boys and an equal chance of 2 girls. Therefore, the remaining 50% of families will have both a boy and a girl.
If the answer to the above problem is 50%, as most people think, then the should be an equal occurrence of Boy-Boy:Boy-Girl families; which, as we can see, is not the case. There are, in fact, twice as many Boy-Girl families as Boy-Boy, or a 33% chance of a second boy.
Question phrased implies first boy is already born. Next child is the only unknown. Chance = whatever chance it is that any individual is male or female.
This is like when you flip a coin 10 times. Which is more likely?
HTTHTTHHHT
HHHHHHHHHH
Equal chance, as no throw has any relation to another.
This is like when you flip a coin 10 times. Which is more likely?
HTTHTTHHHT
HHHHHHHHHH
Equal chance, as no throw has any relation to another.
Its a paradoxical question. what heyheysq said is pretty much as it is. there are 4 possible results.
oldest is a boy, youngest is a boy
oldest is a boy, youngest is a girl
oldest is a girl, youngest is a girl
oldest is a girl, youngest is a boy
knowing that one is a boy, it could be the oldest or the youngest, so either the first, second or last are possible, and only the boy boy one has the other being a boy, so 1/3.
yeah i know it should be 50%, and it is.
oldest is a boy, youngest is a boy
oldest is a boy, youngest is a girl
oldest is a girl, youngest is a girl
oldest is a girl, youngest is a boy
knowing that one is a boy, it could be the oldest or the youngest, so either the first, second or last are possible, and only the boy boy one has the other being a boy, so 1/3.
yeah i know it should be 50%, and it is.
Think of the problem this way:
Instead of thinking "one is a boy" think "they are not both girls". Both mean the same thing.
If they are not both girls, then obviously there is a 33% chance that they are both boys.
The reason most people think that its 50% is because they interpret "one is a boy" as "the first one is a boy". That's not what it means. It means that at least one is a boy, but its still equally likely that it could be either, and half as likely that it could be both.
Instead of thinking "one is a boy" think "they are not both girls". Both mean the same thing.
If they are not both girls, then obviously there is a 33% chance that they are both boys.
The reason most people think that its 50% is because they interpret "one is a boy" as "the first one is a boy". That's not what it means. It means that at least one is a boy, but its still equally likely that it could be either, and half as likely that it could be both.
Oh come on, there is no way that it could be 33%. We aren't considering whether the given child is the oldest or not, so boy-girl and girl-boy are the same.
Wouldn't it just be 50%? If the question was, "A woman has two children, what are the chances that both are boys", then it would be 25%. .5 for each, and .5*.5=.25. However, we've already determined that one is a boy, so there is a 100% chance that the first one is a boy. 1*.5=.5.
50%, and it's completely unaffected by the woman or the number of kids she has.
You see, a human being is created when two cells containing one half of what it takes to create a human being crash into eachother.
These cells are created in the bodies of the father and mother. In the mother's case, her own genetic material, housed in 2 tight little coils shaped like X's, is split into 2 cells, each cell containing a single X.
In the father, his genetic material, housed in 2 coils, one shaped like an X and one shaped like a Y, split apart, and then form 2 new cells, one with an X, and one with a Y.
If the male cell that happens to crash into the woman's cell first happens to be an X, then the resulting baby will have a genetic code of XX, making it a female, like her mom. If it happens to be a Y cell, then the resulting baby will be a boy, having a YX configuration, like his dad.
As each pair of chromosomes are created as a whole and seperated into Y and X sperm in the male, then there should be a relatively equal number of Y and X sperm in any given sample. This could be different for any one test sample, but over a long enough timeline, it will be about 50/50.
So really, none of your information is important and none of it leads to the answer.
You see, a human being is created when two cells containing one half of what it takes to create a human being crash into eachother.
These cells are created in the bodies of the father and mother. In the mother's case, her own genetic material, housed in 2 tight little coils shaped like X's, is split into 2 cells, each cell containing a single X.
In the father, his genetic material, housed in 2 coils, one shaped like an X and one shaped like a Y, split apart, and then form 2 new cells, one with an X, and one with a Y.
If the male cell that happens to crash into the woman's cell first happens to be an X, then the resulting baby will have a genetic code of XX, making it a female, like her mom. If it happens to be a Y cell, then the resulting baby will be a boy, having a YX configuration, like his dad.
As each pair of chromosomes are created as a whole and seperated into Y and X sperm in the male, then there should be a relatively equal number of Y and X sperm in any given sample. This could be different for any one test sample, but over a long enough timeline, it will be about 50/50.
So really, none of your information is important and none of it leads to the answer.
TRICKEY!!!
Look, the options are:
(in order of birth)
Girl then Boy
Boy, then Girl
Boy, then Boy
Girl, then Girl
what is the chance that at least one kid is male? 75%, leaving us with 3 options.
1, both are boys
2, the 2nd kid was designated boy, however the first is girl
3, the 1st kid was designated boy, however the second is girl
there is a 33% chance.
Look, the options are:
(in order of birth)
Girl then Boy
Boy, then Girl
Boy, then Boy
Girl, then Girl
what is the chance that at least one kid is male? 75%, leaving us with 3 options.
1, both are boys
2, the 2nd kid was designated boy, however the first is girl
3, the 1st kid was designated boy, however the second is girl
there is a 33% chance.
