A woman has two children, at least one of which is a boy...

[Solly]

The probability that the other child also is a boy is thus 1/3.

Is this correct or incorrect?

[loinburger]

incorrect.

[MattHiggs]

*runs from Maths Stats*

[Chowlett]

There are 4 equally likely situations, given no info. These are

Bb, Bg, Gb, Gg - where the size of letter indicates oder of birth.

Gg is ruled out by the statement that she has at least one boy. In only 1 case of the 3 remaining does she have 2 boys, so the probability is 1/3

Note - this changes if you specify some defining feature about the stated boy that only one of a pair could possess - such as being the eldest. Then the probability, as expected, becomes 1/2

[Solly]

Loinburger..please explain.

[Rex Little]

With two children there are four equally probable outcomes:
1. Both are boys;
2. First is a boy, second is a girl;
3. First is a girl, second is a boy;
4. Both are girls.

By definition, outcome #4 is excluded, so we have three left. Only one of these has a boy as the other child. Therefore the probability is indeed 1/3.

Edit: Chowlett said the same thing, but got his post in ahead of me.

[orange]

from what I understand, correct, but unfortunately I'm always told that my understanding of prob stat is off

[loinburger]

Buggerall.

[Imran Siddiqui]

What about other alien species?

[Chowlett]

Originally posted by Imran Siddiqui
What about other alien species?

The argument holds assuming they have a 1:1 distribution of male and female births.

[Rex Little]

If we postulate a species which has three sexes, evenly distributed, one of which is male, then the probability is 1/5. Proof is left as an exercise to the student. . .

[Monk]

It's got to be 50% the way I see it, but I'm probably just a stoopid hippy...

[Victor Galis]

It's 1/2. The probability of either offspring being a boy is 1/2. If you know what one is, then the problem reduces to: a woman has one child of unknown gender: the probability it's a boy is: ___

The two births are independent events.

[Imran Siddiqui]

Originally posted by Chowlett
The argument holds assuming they have a 1:1 distribution of male and female births.

But assuming only makes an ass out of you and me .

[Victor Galis]

On the other hand if you are looking at the population of women with 2 children at least one of which is a male, then yes, the probability of the other being a male is 1/3... so it really depends on how the problem is worded and what it's asking for.