Probability riddle

red_fox · 30-01-2008 12:46am

thetaxman wrote: »

Fundamentally flawed argument. These events are independent. How does the fact that she has had a girl increase the chance that she will have a boy for second child. Answer this, are the births independent? If you answer yes, the solution to this problem is 0.5. If you answer no, I have no idea where you are coming from.</p>

It's true if her first child was a girl that the second child is independant and the answer would be 50%.

We only know that at least one is a girl, we assume that all four {BB,BG,GB,GG} are equally likely. If we knew nothing other than she has two children we know there's a 0.75 chance she has at least one boy.

Since we know she has at least one girl the events can only be {BG,GB,GG} each event being equally likely, so a 0.67 chance of at least one boy.

Put another way, if every family had two children we would still expect an even balance (more or less) between boys and girls. There's a 0.75 chance that any given family will have at least one girl, so you expect about 75% of all families to have at least one girl, the rest having two boys. If there was a 50% chance that the unknown child in 75% of all families is a girl then:

0.5 x 1.0 x 0.75 = 0.375 (one of the two children IS a girl, half of 75% of families)
0.5 x 0.5 x 0.75 = 0.1875 (half of the remaining children are girls)
0.5 x 0.5 x 0.75 = 0.1875 (half of the remaining children are boys)

These three numbers sum to 0.75.

The other 25% of families have two boys

1.0 x 1.0 x 0.25 = 0.25.

This accounts 100% of all children but the gender ratio is now 0.5624:0.4375 in favor of girls. The only assumption was that the answer to the OPs question was 0.5. If you use 0.67 you will get the correct ratio but I just wanted to show the contradiction.

Pherekydes · 30-01-2008 12:46am

thetaxman wrote: »

Again, the census is macro not micro, I explained this. Debate my points, don't allude to a flawed website. Troll, give it a rest with your ad-hominem attacks.

The census is macro, and this, remember is a random woman. If you pick any person at random you would expect 50/50 male/female, would you not? If you picked two people at random from the entire population of Ireland, you would expect one male and one female, would you not? If, after picking two people at random (completely independent) and I told you one was female, what would you expect the other to be? Your very sanity depends on the answer you give.

By the way, if you are a troll and he calls you a troll, then it's fair.

Next you'll be shouting conspiracy.

Thomas_S_Hunterson · 30-01-2008 12:48am

thetaxman wrote: »

There are many things which cannot be explained by science alone.

thetaxman wrote: »

This is totally out of balance with nature.

thetaxman wrote: »

In my opinion it would roughly break down to 1/3 BB 1/3GG 1/3BG.

You must be speaking the divinely inspired word of jesus.

Shame that no one else believes you.

When's the crucifiction?

thetaxman · 30-01-2008 12:50am

Slow coach wrote: »

The census is macro, and this, remember is a random woman. If you pick any person at random you would expect 50/50 male/female, would you not? If you picked two people at random from the entire population of Ireland, you would expect one male and one female, would you not? If, after picking two people at random (completely independent) and I told you one was female, what would you expect the other to be? Your very sanity depends on the answer you give.

By the way, if you are a troll and he calls you a troll, then it's fair.

Next you'll be shouting conspiracy.

I would not expect it to be male, you are using basic linear logic.

thetaxman · 30-01-2008 12:51am

2Scoops wrote: »

It doesn't though - it's 25% GG, 25% BB and 50% BG. Check any census you like.

Does the census only include two child families?

2Scoops · 30-01-2008 12:52am

thetaxman wrote: »

I would not expect it to be male, you are using basic linear logic.

We're using logic - no wonder we're getting the correct answer!

Thomas_S_Hunterson · 30-01-2008 12:52am

thetaxman wrote: »

I would not expect it to be male, you are using basic linear logic.

As opposed to multi-dimensional quasi-modal meta-logic?

thetaxman · 30-01-2008 12:54am

2Scoops wrote: »

We're using logic - no wonder we're getting the correct answer!

Again, try to understand the point I made. Its like climbing a ladder, you are moving through the steps, basing your next assumption on your previous.

Pherekydes · 30-01-2008 12:54am

thetaxman wrote: »

I would not expect it to be male, you are using basic linear logic.

As I said, your sanity depends on the answer. Either you're mad or you're trolling.

Where'd you learn your stats, by the way? In the Conspiracy forum?

thetaxman · 30-01-2008 12:55am

Sean_K wrote: »

As opposed to multi-dimensional quasi-modal meta-logic?

Not really, put things can be certaintly be looked at from different perspectives.

2Scoops · 30-01-2008 12:55am

thetaxman wrote: »

Does the census only include two child families?

No, but we can limit our population to families with 2 children.

What's your point, anyway? The same idea holds in families of all sizes - there will be an even distribution of sex amongst children. In families, there will tend to be an even mix of girls and boys. For example, a family of 5 girls will be observed less often than a mix of boys and girls.

2Scoops · 30-01-2008 12:58am

thetaxman wrote: »

Again, try to understand the point I made. Its like climbing a ladder, you are moving through the steps, basing your next assumption on your previous.

The only assumptions we make are that the probability of any given sex is 0.5 and that the sex of each child is independent. The rest are logical deductions.

thetaxman · 30-01-2008 1:01am

2Scoops, if you are making these assumptions you are not applying them.

Pherekydes · 30-01-2008 1:02am

thetaxman wrote: »

Not really, put things can be certaintly be looked at from different perspectives.

Especially in the Conspiracy forum.

Or Green Issues.

2Scoops · 30-01-2008 1:05am

thetaxman wrote: »

2Scoops, if you are making these assumptions you are not applying them.

How so?

ZorbaTehZ · 30-01-2008 1:10pm

The way I would argue it is that if the question also specified that the child was the first/second born then the answer is 50%, but the riddle in its current form means that it's 67%.

gondorff · 01-02-2008 2:20pm

thetaxman wrote: »

Yes, I understand the term, you may not.You are defeating your own argument through this last post. Half the population is male, I agree. Therefore the chance of her second child being male is 0.5. If i toss a coin and get heads, will the chance of getting tails with a second toss reach 0.67? No. Answer my question, are the events independent?

For purposes of calculation of probabilities, each successive coin-toss is independent of the previous one. In this example the two events have already happened.
If someone said they had tossed two coins and the first time came a head, would you then assign 0.5 to the second toss? If so, you are assigning equal probabilities to hh and ht. This runs counter to your argument that 'half the population is male'.

Where's Mdme Vos Savant when you need her?

Pherekydes · 01-02-2008 4:39pm

I think this topic has been exhausted, to most everybody's satisfaction.

For latecomers, thetaxman was a returning banned poster, who was trolling and has since been banned.

I think probability is a very interesting area, and thetaxman actually made people think up new ways to explain an old nugget, until he was spotted as a troll.

I'll lock it, but if anyone has anything further to say (on this specific topic) then feel free to PM me and we'll revisit it.

Probability riddle

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