Mathematical Probability Puzzle

But there is nothing in the problem statement that says ANYTHING about the day of the week the second child is or isn't can or can't be born on.

Also, please show me the correlation/causation between a boy being born on Tuesday and its effect on another child. The sex of a human child is defined by XY chromosomes which give the probably of .5 for both sexes. Playing games with how many days of the week there are does not change that. You can't tell me that it would change again if you said the boy was born in September (12 categories), between Midnight and 12:59AM (24 categories), or on the 132nd day of the year (365.25 categories).

Unless the children are twins, except for the fact that having a boy shows that the couple is capable of having males, the birth events would be independant. Baring androgenous anomilies, and assumuning equal probabilities for male and female, and since we know that the couple has a male childthe probability that they have two male children is 0.5. Birth order is not relevent, there are still two "Equally" probable outcomes for the other child.

^
/ \
F M
/ \
F M

Not all twins are the same gender. Only identical twins must be the same gender.

Neglecting the Tuesday information, the probability of two boys would be 1/3. If we don't know if the boy in question is older or younger, there are three possible scenarios:

BB
BG
GB

So the probability would be 1/3 that both are boys. If we bring the Tuesday information into the equation, then mathematically I agree with Alex:

alex_bell said:

My reasoning is as follows:

The "Tuesday Boy" can be either the first or second child.

So the other child can be either a boy or a girl born on any day of the week. So the availabel combinations are(bTu = Boy Tuesday, gMo = Girl Monday etc):

Code:

1st child	2nd Child
bTu	          gMo
bTu	          gTu
bTu	          gWe
bTu	          gTh
bTu	          gFr
bTu	          gSa
bTu	          gSu
bTu	          bMo
bTu	          bTu
bTu	          bWe
bTu	          bTh
bTu	          bFr
bTu	          bSa
bTu	          bSu
gMo	          bTu
gTu	          bTu
gWe	          bTu
gTh	          bTu
gFr	          bTu
gSa	          bTu
gSu	          bTu
bMo	          bTu
bTu	          bTu
bWe	          bTu
bTh	          bTu
bFr	          bTu
bSa	          bTu
bSu	          bTu

So there are 28 combinations above which result in 14 boys and 14 girls.

However the combination bTu is repeated so should be removed resulting in 27 total combinations 13 of which are boys and 14 girls, i.e. 13/27

Click to expand...

smryan said:

I have to agree with Tom's login here. But if Tuesday matters its a trick question.

Click to expand...

The day is important

trainerbob said:

The probability of two boys is 1/3. Please don't ask me how. I don't have time right now to go through the process again.

Click to expand...

and the answer is not 1/3. Keep trying.....

iamnototep said:

Your new mathematics-obsessed friend says to you, "I have two children. One is a boy born on Tuesday. What is the probability I have two boys?"

The first thing you think to ask him is, "What the heck does Tuesday have to do with it?"
"Everything!", he replies...

So what is the probability?

Click to expand...

The day is important ONLY if it was used to pick you out of all parents.

If you choose a random fact of the form "One is a [boy/girl] born on [day of week]" that was true of at least one of your children, the answer is 1/2. If you were picked to tell us this fact because you had a boy born on a Tuesday, the answer is 13/27.

Probability is not determined by merely counting cases. It is determined by summing the probability that each case would produce the observed result. So, while it is true that there are 27 cases where a family of two includes a boy born on a Tuesday, and it is also true that 13 of those 27 include two boys, it is not true that the probability a parent of these families would tell us "I have two children, and one is a boy born on Tuesday" is the same in all of those cases. It is 1 only when both children are boys born on Tuesdays. It is 1/2 in all of the other cases. So the correct answer, to the question as asked, is (1+12/2)/(1+26/2)=7/14=1/2.

Now, if I had asked you "I know you have two children, but is one a boy born on Tuesday?" and you answered "yes," then 13/27 is right. But nothing in the problem as stated suggests that. And the 13/27 answer is unintuitive because everybody treats "Tuesday" as an observation, not a requirement.

The answer when you said only "I have two children, and one is a boy" is also 1/2 for similar reasons.

0% chance as 'one is a boy born on a tuesday', the wording suggests the other is a girl.

Thats what I think anyway

I missed this the first time around and haven't looked through all of the posts, but it seems to me that the fact that Tuesday is significant means that the solution involves the probability of a second child being a boy or girl when the first was a boy born on Tuesday. In other words, you first have to enumerate the number of boys born on Tuesday and then how many of their single siblings were boys or girls. Nonetheless, for pure probability purposes, the sex of the second child is an independent event.