Google Interview Question - Probability

[joey122]

It seems to me that they are all Google quality.

The final quantity sought in the question is the proportion of boys to girls. Given that:

• The probability of a child of a given sex is 0.5 for any given pregnancy;
• The probability of a child of a given sex is independent of the outcome of any other pregnancy;

...then it comes down to the same thing as people tossing a coin and stopping when it lands on heads. If x people toss a coin, then x/2 will land on heads and stop tossing, and x/2 will land on tails and continue to toss. (Ooh-er, Missis!)

So the next cycle will be (x/2)/2 land on heads, and (x/2)/2 get tails.

And then ((x/2)/2)/2 get heads and ((x/2)/2)/2 get tails.

The probabilities of each outcome remain equal whatever number of iterations you choose, as no previous iteration can affect the outcome of a subsequent iteration, and no single outcome within a given iteration can affect another outcome within the same iteration. Although the value of x is halved on each iteration (and is therefore the only variable quantity), the probability of each outcome remains at 0.5 for each iteration. As the only variable is independent of the relative proportions of the outcome, it is obvious that the relative proportions will remain unaltered as the series is summed: 0.5 heads, 0.5 tails.

I don't know if Google actually use this question (I doubt it - there's a lot of crap spread around about interview questions used by top companies) but insofar as it has any interest, it's in that by introducing the question of human reproduction it might throw people off the scent, as people have a vague feeling that it must be quite complicated if it involves something so important. This is a purely psychological thing, and given that the question can be equally well put in terms of coin-tossing, it is I suppose possible that it might be used to see if a victim can avoid being distracted by irrelevant circumstances and focus on the underlying principles.

But to be honest, if I went for an interview at somewhere like Google and they started asking me crap like this, I'd tell them to stop pissing about and get on with it.

I dont think that this is independent - Surely if a family has one girl then the probability of a boy next increases??

Similarly if I told you that I tossed 100 coins and each toss was fair and resulted in a tail would you not feel more bullish expecting a heads next??

[NickFitz]

I dont think that this is independent - Surely if a family has one girl then the probability of a boy next increases??

Similarly if I told you that I tossed 100 coins and each toss was fair and resulted in a tail would you not feel more bullish expecting a heads next??

Nope - the outcomes are independent. What happens in one conception will have no effect on what happens in a subsequent conception. If you can demonstrate some mechanism by which it could have an effect, you're in line for a Nobel Prize for Medicine - or possibly Physics, as you will have overturned all known laws of cause and effect.

In the same way, the probability of any individual toss of a fair coin coming up heads is always 0.5, no matter what has happened before.

Not that relevant, but Derren Brown demonstrated a coin being tossed and coming up heads twelve times in a row. He then admitted that they had to film him tossing coins for something like eight hours before it happened - but happen it did

[EternalOptimist]

nope. some species have one sex of offspring depending on the incubation temperature.

[NickFitz]

nope. some species have one sex of offspring depending on the incubation temperature.

The question specifically refers to humans. Anyway, the biology stuff is just a distraction: they're looking for an ability to get past the irrelevancies.

[AtW]

What this stupid question has got to do with the job in question?

I remember on one of my job interviews (~10 years ago) I was made to write C code using pen, maybe a few years after imminent SKA success I'll be just attending interviews for a laugh or two

[EternalOptimist]

The question specifically refers to humans. Anyway, the biology stuff is just a distraction: they're looking for an ability to get past the irrelevancies.

wrong again Nick.
Its a well know fact that the liklihood of a boy increases if the female gets on top

thank you.

[threaded]

It has been shown that in an area with a female skew to the population the number of male births goes up, and vica versa.

They don't know the mechanism, just the statistics.

[EternalOptimist]

It has been shown that in an area with a female skew to the population the number of male births goes up, and vica versa.

They don't know the mechanism, just the statistics.

I just explained the mechanism, female on top equals more boys.

its a well known fact

[Zippy]

Yeh, but it is not random but genetic on male side. In a population of 50 million say, what is to stop a woman having 96 billion girls before they get to a boy? Well, perhaps not 96 billion but one every 9 months from age 8 to age 70, that's 84 of em. Gawd, she'd have a fanny like the channel tunnel.

I think you'd have huge problems getting anywhere near the missus after child no 4
I believe sperm production in males is not entirely random (something I read, can't prove it) so the odds for a particular couple producing a male (or female) would not be 50/50

[minestrone]

In a country in which people only want boys…
…every family continues to have children until they have a boy. If they have a girl, they have another child. If they have a boy, they stop. What is the proportion of boys to girls in the country?


Answers

There is no answer, they want to see your thought process getting to an answer that cannot be found.

You are meant to be asking questions like "can you tell me what is the proportion of girls to boys born in this country?", "can you tell me what the proportion was before this rule is applied?" "How many families have reached the objective and how many have not?" "how many families are there?" instead of plugging in estimates to an equation like some of you have.

Myself, a degree trained engineer would grasp that but as most of you are not mathematically inclined then I see you are struggling with basic stats to answer a chaotic situation.

You have all failed.