Question

A man has two children.he tells that one of them is a son.what is the probability that the other one is also a boy

Answer 1

gg
bg
gb
bb

3 out of 4

Answer 2

lol ... 1 out of 4 doh!!

Answer 3

You so silly!

Answer 4

1/2

Answer 5

I got It , it is 1/3

Answer 6

Yes, 1/3

Answer 7

that was my next correction :)

Answer 8

bg is the same as gb since we aren't concerned with the order.

Answer 9

i saw it as 3 options for b? and 1 option for bb

1/3

Answer 10

'he tells that one of them is a son'
bb
bg
so,1/2
if my answer is wrong,can anyone explain

Answer 11

you have 4 options for children to begin with

gg
gb
bg
bb

we know one of the is a b already;

gb
bg
bb

out of these we need to determine whats the probability that we get bb

well; its 1 out of 3

Answer 12

oh thanks i was confused

Answer 13

it might be better expressed as P(b|b) or some such

Answer 14

1/4
--- = 1/3
3/4

Answer 15

i dont know my question is dumb or not
but i want to clear my doubt
@amistre or anyone
we know that one them is a boy
then how we can take g,g(girl,girl)

Answer 16

In thinking about this further I'm actually of the opinion that the answer is 1/2 as you suggested originally.

We don't care about what order the kids were born or anything like that. It's just a combination problem.

It will be one of:

2 girls
1 boy and 1 girl
2 boys

From this we already know that there is at least 1 boy. Therefore the only possibilities are:

1 boy and 1 girl
2 boys

And of that we want to know the probability of 2 boys. It is 1/2.

Answer 17

If he hadn't said that one was a son already it would only be a 1/3 probability.

Answer 18

so,in this case the answer is 1/2

Answer 19

I believe so.

Answer 20

I was thinking about it in terms of

2 girls
1 boy 1 girl
2 boys

and finding the probability of 2 boys.

Answer 21

but we already know there is 1 boy, so that restricts the possible options.

Answer 22

thanks polpak

Answer 23

Thank you for pointing out the mistake.

Answer 24

Since this is a probability problem, I think we should include bg, and gb as two cases, or at least mention that the probability of bg/gb is twice the probability of bb. It is of course 9 hours later though, so I don't expect this to be useful information if you were doing your homework :)

Answer 25

As long as one of them aint borned on a tuesday; 1/3 should fit the bill :)

http://www.sciencenews.org/view/generic/id/60598/title/Math_Trek__When_intuition_and_math_probably_look_wrong

Answer 26

I like this paragraph:

-----------start quote-------------

Gardner himself tripped up on his simpler Two Children Problem.

Initially, he gave the answer as 1/3, but he later realized that the problem is ambiguous...

Suppose that you already knew that Mr. Smith had two children, and then you meet him on the street with a boy he introduces as his son. In that case, the probability the other child is a son would be 1/2, just as intuition suggests.

On the other hand, suppose that you are looking for a male beagle puppy. You want a puppy that has been raised with a sibling for good socialization but you are afraid it will be hard to select just a single puppy from a large litter. So you find a breeder who has exactly two pups and call to confirm that at least one is male. Then the probability that the other is male is 1/3.

--------end quote-----------