# What's the odds of getting two pairs out of...



## ecichlid (Dec 26, 2012)

What's the odds of getting two pairs out of 5 random frogs, 6 or even 7 random frogs. 

Last time I purchased 5 frogs I did get two pairs out of them. I'm not counting on being lucky this time around. I would like to know my chances before pulling the trigger on some Southern variabilis.


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## CosmicFool (Jul 9, 2014)

Poison Dart Frogs For Sale

there is a nice little chart on that link for one pair
5 frogs = 94% which I guess would leave you with a 75% to get a pair on the remaining 3 frogs unless the math doesn't work out that way (odds can get tricky)


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## ecichlid (Dec 26, 2012)

So is that a 70.5% chance on five frogs?


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## froggorf (Nov 22, 2008)

I don't know about the exact math but speaking from experience with southerns they have pretty even sex ratios. From 4 frogs I got 2.2 and from a trio I got 2.1, luckily they're readily available and you could easily trade to get the ratio you like. That said, if you bought six frogs and didn't end up with at least 2 of each sex that's some bad luck


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## SMenigoz (Feb 17, 2004)

There are some species such as Azureventris that has never heard of the probability chart.


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## ngeno626 (Nov 14, 2013)

It definitely depends heavily on the species, mathematically the odds will always be the same, however many morphs, pumilio in particular, tend to be Male or female heavy.


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## ecichlid (Dec 26, 2012)

Thanks guys, but I was hoping some math wiz would give a confident answer.


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## khoff (Feb 18, 2004)

You are looking for Binomial Probability. The formula is a bit....technical. So I find it easiest to use an online Binomial Probability Calculator:
Binomial Probability Calculator

ASSUMPTION: 50/50 probability of any single frog being male/female

Probability of 2 males of 5 total frogs: 0.3125
Probability of 3 males of 5 total frogs: 0.3125
Sum of the 2 above probabilities: 0.625 = *62.5% probability you will get 2 pairs out of 5 frogs*

Probability of 2 males of 6 total frogs: 0.234
Probability of 3 males of 6 total frogs: 0.3125 (31% probability of 3 pairs out of 6 frogs)
Probability of 4 males of 6 total frogs: 0.234
Sum of the 3 above probabilities: 0.78 = *78% probability you will get 2 pairs out of 6 frogs*

Hope this helps


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## ecichlid (Dec 26, 2012)

Thank you Kevin! Would you *please* go just one step further to 7 frogs? I checked out the link you included, looked Greek to me!


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## froggorf (Nov 22, 2008)

Using Kevin's formula:

Probability of 2 males of 7 total frogs: 0.164
Probability of 3 males of 7 total frogs: 0.273
Probability of 4 males of 7 total frogs: 0.273
Probability of 5 males of 7 total frogs: .164
Sum of the 4 above probabilities: 87.4% probability you will get at least 2 pairs out of 7 frogs

I was actually using the same formula last night but thinking about it in a different way, didn't know you could add probabilities (Thanks Kevin!)


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## ecichlid (Dec 26, 2012)

Thank you! Now that I know the numbers, I'm going with 7.


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## ngeno626 (Nov 14, 2013)

Woah to many numbers. I need a beer after this thread.


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## FroggyKnight (Mar 14, 2013)

Ugh, probabilities. I just finished a stats class last quarter and it was hell. You do have the right answer, though. I pulled out those wretched notes to double check 



ngeno626 said:


> Woah to many numbers. I need a beer after this thread.


I feel ya....


John


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## Scott (Feb 17, 2004)

What are the odds of getting all pairs with 7 frogs?

(In other words - always buy even numbers of frogs  )

s


ecichlid said:


> Thank you! Now that I know the numbers, I'm going with 7.


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## FroggyKnight (Mar 14, 2013)

Scott said:


> What are the odds of getting all pairs with 7 frogs?
> 
> (In other words - always buy even numbers of frogs  )
> 
> s


Eh, maybe not _always_. Some prefer to keep their frogs in male or female heavy groups/trios. It's just personal preference 


John


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## Wusserton (Feb 21, 2014)

I bought 4 vitattus from Josh's and all are doing great but all are female ...that was at 88% chance of getting a mix, if anyone has a male let me know I'll take him but will have to wait for spring thaw/shipping if your willing to hold him, I got lucky on my anthonyi rio pair I bought for my already established male, one male one female in that pair so it would seem but early, all three seem to be getting along at feeding but sometimes I see my 3 yr male hopping on the back of the smaller of the two I bought (just starting to turn red) so Im thinking aggression is happening and will seperate soon, its a shame too because I searched and searched for a definate female and came up empty so I bought 2 juvies on a chance, and have 2:1, watching closely but will build another tank soon if needed ...oh darn, another tank lol


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## Baltimore Bryan (Sep 6, 2006)

Glad the math is sorted out. Now that (I think) the original question is well answered, I hope it's ok if I bring up a slight twist to the discussion based off Scott's earlier response:



SMenigoz said:


> There are some species such as Azureventris that has never heard of the probability chart.


I know azureiventris are known to have unusual sex distributions. I've also heard people say that anecdotally some other captive bred frogs show disproportional sexes (like azureus, pumilios are males heavy, etc...) Does anyone have any data or studies regarding the sex distribution of these frogs? I had always thought that the sex was determined at fertilization for frogs, but the azureiventris in particular seem to produce a highly statistically unusual ratio of males/females. 
I know there have been hypotheses that azureiventris offspring are affected by temperature while tadpoles. Does anyone have any other info on this? Or on any other frogs that may seem to produce disproportionate male/female ratios? 
I saw this thread- http://www.dendroboard.com/forum/general-discussion/6585-when-sex-dart-frog-determined.html
It has some good info and possibilities to explain these results, such as the frogs could be expressing the wrong sex (i.e. have female genes but aren't "females"), or that something could be selectively pressuring one sex during development so that most adult survivors are the other sex. Anybody have other experience or data on this?
Thanks,
Bryan


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## ecichlid (Dec 26, 2012)

Scott said:


> What are the odds of getting all pairs with 7 frogs?
> 
> (In other words - always buy even numbers of frogs  )
> 
> s



I'm hoping for three pairs and a hermaphrodite.


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## Wusserton (Feb 21, 2014)

I read that also, and I would think initially it would be a genetic variance of some sort but maybe temp or lack of suitable breading partners would play a roll, your talking different sized enclosures, simulated environmental factors ie: hot cold wet dry, withholding sexes, basically years and years of study to try and even pinpoint a possible cause ...if you figure this out it would be a scientific breakthrough and should be published and documented and thats probably per species! Im no genius and would never presume to be one but this sounds like something that would take years of trial and error in a lab setting to even hope of getting an answer for ...but, fortunately we have nature, and it seems to figure it out ...at least in the wild. We can go all day long in captivity and hope and aspire to achieve what nature gives us but fact being every species does best in its natural element human influence aside. That being said we as humans are ruining everything and thats the reason why some of us are here, to protect and continue these lines, and in that this is probably one of the noble quests of our age, this is something that countries should be pouring money into in my opinion.


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## jsilva (Nov 2, 2014)

To avoid so many numbers and formulas I would just wait for somebody who sells a proven breeding pair 1.1 and you all set


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## ecichlid (Dec 26, 2012)

jsilva said:


> To avoid so many numbers and formulas I would just wait for somebody who sells a proven breeding pair 1.1 and you all set


Did you read any of the post?? We were discussing two pairs. And yes, we all know that we can purchase 1.1 and then another 1.1. So, thanks for your insight.


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## epiphytes etc. (Nov 22, 2010)

Baltimore Bryan said:


> Glad the math is sorted out. Now that (I think) the original question is well answered, I hope it's ok if I bring up a slight twist to the discussion based off Scott's earlier response:
> 
> 
> 
> ...


I know this has been discussed here before, but since I'm on my phone, I can't really look for it easily. I'm pretty sure it has been shown that in azureiventris, sex is dependent on temersture at the time of fertilization, and not during tadpole development.


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## Baltimore Bryan (Sep 6, 2006)

epiphytes etc. said:


> I know this has been discussed here before, but since I'm on my phone, I can't really look for it easily. I'm pretty sure it has been shown that in azureiventris, sex is dependent on temersture at the time of fertilization, and not during tadpole development.


I hadn't heard the part about time of fertilization, not tadpole development, being more important in sex determination as a function of temperature. I did a quick search here and elsewhere and didn't find much. I would be interested in hearing more about others' experiences with this, and in addition, if there is any scientific data to support the anecdotal information or explain these results. It just strikes me as odd that these frogs in particular seem to be the only ones with wacky sex ratios in captivity, but then again I know they are also different from most of the other frogs we keep in the hobby in some other ways.
Bryan


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## Spaff (Jan 8, 2011)

I actually attempted a small pilot study on sex ratios in H. azureiventris, and it ultimately got scrapped because we couldn't acquire enough females to make the results statistically significant. At the time of my research into it, TSD has never been observed in frogs (in any way). 

One potential hypothesis for the naturally skewed sex ratio (if this occurs in Peru) is that males are more easily predated upon because they venture out into the open when calling for mates. It has been suggested that this species does not sequester alkaloids through its diet, so predation may be higher since these have low toxicity or none at all.


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## LizardLicker (Aug 17, 2012)

This is one of the reasons I don't like math... Those percentages never quite work out for me it seems. 

I also had a recent conversation with someone that got an order of 10 frogs that aren't what I would call cheap. Not extremely rare or anything though. 

His ratio? 9.1.....  I am not going to say who it is because I don't know if they would mind or not. However, randomness can rear its ugly head at the worst times.


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## frogfreak (Mar 4, 2009)

LizardLicker said:


> His ratio? 9.1.....


Perfect for a group of Tincs.  

BTW, I find Tincs are male heavy. Anyone else?


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## markpulawski (Nov 19, 2004)

Actually I have been doing the math for a couple of days now, if you were to get 7 frogs the odds of getting 2 pair are GOOD. Don't thank me, I was just lucky and get access to one of those Super Computers and I entered the data.


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