I think it's actually been 2.5 years, this time.

[theweaselking]

It's That Time Of Year Again!

You run a zoo! Your head cloning scientist says she has two new baby velociraptors to show you. You fire her immediately for CLONING VELOCIRAPTORS, but you're still stuck with a few million dollars worth of baby animal that you can't necessarily afford to trash out of hand.

"Well", you think, "at least if they're all male, they can't breed with my *existing* population of 100%-male no-frog-DNA screw-you-Crichton velociraptors. Exactly 50% of all cloned velociraptor babies are male! Maybe I can keep them."

So you call your *new* head cloning scientist and ask *her* if at least one of the babies is male. She is briefly confused about the nature of your query, and then she has to bone up (no pun intended) on sex determination of infant cloned dinosaurs, but then she comes back and says "Yes! One of the babies is male!"

While this is technically the question you asked, this is not the answer you *wanted*. So, facing the loss of millions and losing your temper, you thank her and hang up so you can think.

And so, we reach your question: What are the odds that the second velociraptor is also male?

[EDIT: Your question was "is at least one male?". Her answer is "Yes! At least one is male!". This is not a trick based on the wording from your second-best cloning scientist.]

[EDIT2: Is is not a wording-based trick of any sort. You have two babies, each with a 50% chance of being male and a 50% chance of being female. One of the babies is male. What are the odds that the other baby is also male?]

Comments

[dreamshade.livejournal.com]

I'm not even going to answer this one because this one is old, old, old, old (at least, in forms that don't deal with velociraptors), and anyone who gets it wrong is very new to math-based brain teasers.

[theweaselking.livejournal.com]

The raptors and snark are there to make it harder to Google.

[pope-guilty.livejournal.com]

As I've said, I'm fairly ignorant of probability, and my ignorant guess would be 50%. The odds of throwing heads or tail on a single coin throw are 50% regardless of previous throws, and so it seems to me that knowing that at least one of the raptors is male doesn't have any bearing on whether the sex-unknown raptor is male or female. So I'm saying 50%, with no particular confidence and based on nothing more than analogizing from another case in which you know one outcome but not another.

[dreamshade.livejournal.com]

*bzzzzzzzzzzzzt* Thank you for playing our game! We have some lovely parting gifts for you~

[scifantasy.livejournal.com]

33%.

There are four scenarios, as follows:

Velociraptor Baby #1 (henceforth, VB1) is female, Velociraptor Baby #2 (henceforth, VB2) is female.
VB1 is male, VB2 is female.
VB1 is female, VB2 is male.
VB1 is male, VB2 is male.

From the data we have, we know the first scenario is impossible.

Therefore, the question becomes, of the three scenarios, how many have two males? Answer: one. Hence, 1/3, or 33%.

[theweaselking.livejournal.com]

I will note, for the record, that the last time I asked this question, you got it wrong.

Are you *sure*?

[cuddlycthulhu.livejournal.com]

33%?

[harald387.livejournal.com]

This isn't the first time I've been asked it.

This also isn't the first time I've gotten it wrong.

And it isn't the first time I've felt like an idiot for not being able to figure it out.

[theweaselking.livejournal.com]

Have you not seen any of the Jurassic Park movies?

Cloning raptors was a mistake the first time, but you can't just destroy millions of dollars of R&D and immensely valuable live products. So you keep them and you hope your liability insurance accepts your disclaimers when the raptors get out, and you definitely don't let them breed.

And then your head scientist comes to you with "Hey, look, more raptors! I've made them BETTER!" Oh, fuck yes, you fire that person.

[cheshire-bitten.livejournal.com]

Well I am amused.

[pope-guilty.livejournal.com]

Oh, Angelspit. :D

[kafziel.livejournal.com]

Well, that depends. If this is a rephrased Monty Hall problem, then it's 1/3rd. If she only tested one and that one turned out male, and she didn't test the other at all, then 50%.

[theweaselking.livejournal.com]

Your answer is wrong!

(I'm not saying how, yet)

[cosmiccat.livejournal.com]

Okay, going to bite, even though these things are invariably Schmuck Bait:

0%. Exactly 50% of all cloned velociraptor babies are male. This is because there are only two cloned velociraptor babies in existence, they are in your lab, and only one is male.

[theweaselking.livejournal.com]

Hah!

Great answer, but not what I intended. 50% of cloned velociraptor babies are male, by virtue of each cloned velociraptor having a 50/50 chance of being male/female.

[spawnofweevil.livejournal.com]

If the velociraptor babies were both cloned from the same source, I'd think they'd both be male, what with being clones? Or are they clones of different velociraptors...?

[theweaselking.livejournal.com]

Haven't you seen Jurassic Park?

(More seriously: 50% of the output of your cloning effort are male, 50% female. IT IS MAGICAL.)

[blake-reitz.livejournal.com]

The answer is NATURE FINDS A WAY!

[unknownpoltroon.livejournal.com]

0%. Jeebus told me there was no such thing as dinosaurs.

[coyotegoth.livejournal.com]

100%, assuming they're cloned from the same source material (and if you have more than one adult Deinonychus- called "Velociraptors" in Creighton's book, although real Velociraptors would be waist-high to a man, if that- roaming around, then you have more urgent things to be doing then firing geneticists). If not- if the Dinosaur Gender Fairy shook things up so it could go either way- then 50%.

[pope-guilty.livejournal.com]

Reminds me of "The Gun is Your Skill List" from The Munchkin's Guide to Power Gaming.

"What kind of animal is that?"
*BLAM*
"A dead one."

[opaqueplanet.livejournal.com]

This is Math Problem, not Science Problem.
I fail at math problems unless I am given Formulae (or can figure out what formula to use. Which I can't, here).

If it were Science Problem:
Assume "clones" are not "real" clones, or they'd all be male.
Assume male-male reproduction.
P= XY XY
F= XX XY XY YY
Offspring are 25% male, 50% female, and 25% nonviable
Knowing that one of the babies is male, the chance that the other is male is 1/3 (assuming it's hatched).

But you said that odds are 50% male/female, so again, not Science Problem. Math Problem.

[cacahuate.livejournal.com]

I like your method.

[sparkindarkness.livejournal.com]

50%

If exactly 50% of all cloned velociraptors is male then every velociraptor has a 50% chance of being male. The established maleness of the first doesn't make the second less likely to be male any more than my flipping a coin and it coming up heads makes tails more likely if I flip again


Ugh and I should read comments before commenting

[kadath.livejournal.com]

1:3

There are three possible combinations:

female female
male female
male male

The fact that the scientist has confirmed one of the hatchlings is male is a red herring. What you know about the situation doesn't affect the probabilities. Since the problem specifies the sex is a binomal trial on a fair coin, you're looking at one chance in three.

[opaqueplanet.livejournal.com]

1/3 is the odds that BOTH are male.

The odds that the second one is male is still 1/2. It's always 1/2, because the odds that ANY cloned velociraptor is male is 50%.

The wording is important, and I think theweaselking may have messed that up if he intended the answer to be 1/3.

Odds that 1st one is male (before testing): 50%
Odds that 2nd one is male given the 1st one is male: 50%
Odds that both are male: 33%

[cacahuate.livejournal.com]

If you just know that at least one of the babies is male, all you really know is that the babies are not both female. So the problem can be rephrased: The babies are not both female. What is the probability that they are both male?

The possibilities for any two babies that you know nothing about are

FF
MF
FM
MM

With the information we have, we can eliminate the first possibility, leaving the other three. So, the probability that they are both male is 1/3.

[kadath.livejournal.com]

It's combinations, not permutations. The order doesn't matter.

[biomekanic.livejournal.com]

My answer to put the little bastards in enclosures in different locations so there's no way in hell they can breed.

There, problem solved.

Now, I'm going shopping.

[silmaril.livejournal.com]

One-third.

We've Baby A and Baby B, and four different combinations: (A,B)=(M,M), (M,F), (F,M) and (F,F). Given that one of the babies is male, but not knowing which, we must have one of the first three configurations. Only combination 1 gives the other baby male also, no matter which baby she looked at.

Or, if you want overkill, my event space is {(M,M),(M,F),(F,M),(F,F)}. Let A="at least one raptor is male"={(M,M),(M,F),(F,M)}; P{A}=3/4 in my event space. Let B="both raptors are male"={(M,M}}; P{B}=1/4. Then probability of B given A, P(B|A), which is what you're asking for, is P{A|B}*P{B}/P{A}=1*(1/4)/(3/4)=1/3. (P{A|B}=1 by definition, since B is a subset of A.)

[drjon.livejournal.com]

"You have two babies, each with a 50% chance of being male and a 50% chance of being female."

Baby #2 has, by your assertion, a 50% chance of being male.

However, you confused matters earlier, when you said

"Exactly 50% of all cloned velociraptor babies are male!" and "Yes! One of the babies is male!"

By that tell, baby #2 has a 0% chance of being male.

What are the chances? Ask me when you've really got a cloned velociraptor or two.

[theweaselking.livejournal.com]

Each baby had a 50% chance of being male.

Baby #1 rolled his dice and came up "male".
What are the odds that baby #2 got that same result?

[eruvadhril.livejournal.com]

The odds that the other baby is also male are 50%, just like every other baby born (assuming no genetic or reproductive abnormalities in both parents). Unless the velociraptor was cloned from the exact same DNA as its brother, in which case it will definitely be male and genetically identical to its brother.

[theweaselking.livejournal.com]

We're using magic movie-style clone-tech here, where any given baby's sex is randomly determined.

[falconwarrior.livejournal.com]

The odds of any single cloned raptor being male are one in two.
The answer to this question is one in three.
The odds of any pair of cloned raptors both being male are one in four.

[mejoff.livejournal.com]

50%

[xomox.livejournal.com]

50%, as they're independent. Just like rolling dice, the result of one does not entangle the roll of the other.

[kafziel.livejournal.com]

If the question was "Raptor A is male, what are the odds that Raptor B is male too?" then you'd be right. But that's not the question. The question is "Of Raptor A and Raptor B, at least one is male. What are the odds that both are male?" You could have Raptor A being male and Raptor B being female, you could have Raptor A being female and Raptor B being male, and you could have both being male. All of these outcomes are equally likely. So the odds are 1/3rd.

[chaosrah.livejournal.com]

Initially I would think it would be .5 x .5 = .25
But I'm half awake and did not sleep well, I'm thinking it might be more complicated than that. But I tend to over-think.
I was about to put a secondary explanation, but I think I will opt to go back to sleep.