A Math Question
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 triviawayne
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A Math Question
My wife decided to buy chickens. She is hoping she doesn't end up with a rooster.
She said the lot of birds the store gets their supply from claims 80% are hens.
Since she bought 4 birds, I think the odds are 625:1 that one of them is a rooster.
Am I correct?
She said the lot of birds the store gets their supply from claims 80% are hens.
Since she bought 4 birds, I think the odds are 625:1 that one of them is a rooster.
Am I correct?
Total game show career losings = $171,522
Re: A Math Question
Trying to dust the cobwebs off this part of my brain before working with numbers, but I'm concerned about your phrasing "that one of them is a rooster"triviawayne wrote: ↑Tue Jun 30, 2020 3:09 pmMy wife decided to buy chickens. She is hoping she doesn't end up with a rooster.
She said the lot of birds the store gets their supply from claims 80% are hens.
Since she bought 4 birds, I think the odds are 625:1 that one of them is a rooster.
Am I correct?
Is that the problem or "that at least one of them is a rooster" You could get up to four.
Maybe work the other way....
The chance of getting 4 hens, 80%*80%*80%*80% = 41%, so you have a 59% chance of getting at least one rooster?
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 selwonKttaM
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Re: A Math Question
Are they African or European chickens?
I had a dream that I was asleep and then I woke up and Jeopardy! was on.
 triviawayne
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Re: A Math Question
For the first part  we're hoping none of them are roosters.Volante wrote: ↑Tue Jun 30, 2020 3:19 pmTrying to dust the cobwebs off this part of my brain before working with numbers, but I'm concerned about your phrasing "that one of them is a rooster"triviawayne wrote: ↑Tue Jun 30, 2020 3:09 pmMy wife decided to buy chickens. She is hoping she doesn't end up with a rooster.
She said the lot of birds the store gets their supply from claims 80% are hens.
Since she bought 4 birds, I think the odds are 625:1 that one of them is a rooster.
Am I correct?
Is that the problem or "that at least one of them is a rooster" You could get up to four.
Maybe work the other way....
The chance of getting 4 hens, 80%*80%*80%*80% = 41%, so you have a 59% chance of getting at least one rooster?
For the second part...that was one of the ways I thought of it too, but then it just didn't feel like I did the math correct?
This is where statistics make me just think "HUH????????"
I guess what I'm looking for is some hope. What we want are ZERO roosters. What are the chances we have ZERO roosters?
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 triviawayne
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 badgerfellow
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Re: A Math Question
Wouldn't the individual probability of each subsequent fowl not being a rooster change though, and thus the overall probability of not picking a rooster be dependent on number of fowl? Example: If there are 20 hens/roosters to begin, there are 4 roosters and 16 hens. Say you've picked a hen to begin; that one is now out of the pool to select from for round 2. Next fowl now has a 15/19 probability of not being a rooster. Your probability of not picking a rooster in 4 tries is now (16/20)*(15/19)*(14/18)*(13/17), or about 37.6%. Bump up the available flock to 100 birds, and the probability increases to 40.3%.
Re: A Math Question
"Yes" but the store themselves have stated the probability is already 80/20 so they are probably maintaining a large enough stock that removing a chick keeps the ratio at effectively 80/20. You're getting four out of the high hundreds maybe even thousands.badgerfellow wrote: ↑Tue Jun 30, 2020 5:00 pmWouldn't the individual probability of each subsequent fowl not being a rooster change though, and thus the overall probability of not picking a rooster be dependent on number of fowl? Example: If there are 20 hens/roosters to begin, there are 4 roosters and 16 hens. Say you've picked a hen to begin; that one is now out of the pool to select from for round 2. Next fowl now has a 15/19 probability of not being a rooster. Your probability of not picking a rooster in 4 tries is now (16/20)*(15/19)*(14/18)*(13/17), or about 37.6%. Bump up the available flock to 100 birds, and the probability increases to 40.3%.
Course, if wayne wants to name names so we can research the size of this fowl operation...
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Re: A Math Question
Embarrassing moment: The city boy here had to look up just to make extra sure that hen/rooster were female/male chickens.triviawayne wrote: ↑Tue Jun 30, 2020 3:09 pmMy wife decided to buy chickens. She is hoping she doesn't end up with a rooster.
She said the lot of birds the store gets their supply from claims 80% are hens.
Since she bought 4 birds, I think the odds are 625:1 that one of them is a rooster.
Am I correct?
But no, you're off. You computed the odds of getting "Oops, all roosters!".
If 4/5 are hens, then the chance that you get 4 hens are (4/5)^4 = 0.4096, or about 41%. So, 100%  41% = 59% of the time, you get at least one rooster.
I'm assuming that we're picking hens out of an infinitely large vat of chickens so that "with replacement vs without replacement" doesn't matter. The problem is slightly different if you're picking 4 chickens out of a set of 100 chickens, with 80 hens...but it's probably close. It's VERY different if you're selecting 4 chickens from a set of 8 hens + 2 roosters.
I'm also assuming that we're picking independently. That means that when you pick a hen or a rooster for your first pick, your next pick is still 80% hens  it's not like picking a hen will make a rooster come to the top of the vat to valiantly try to rescue his mate.
For the rest of the odds, we can use the binomial theorem:
(0.8h + 0.2r)^4 = 0.4096h^4 + 0.4096h^3r + 0.1536h^2r^2 + 0.0256hr^3 + 0.0016r^4
Note that your odds of getting all hens is the SAME as the odds of getting 3 hens and a rooster. Why? Well, when you pick HHHR in any order vs HHHH, swapping in an R will decrease your odds by (80 / 20) = 4. But you can also rearrange HHHR to HHRH, HRHH, RHHH, which multiplies your odds by 4. The two factors basically cancel each other out.
As another example, for 2 roosters and 2 hens, your odds of getting them in the exact order HHRR is (4/5)(4/5)(1/5)(1/5) = 16/625. But you can move those two hens into any position  HRHR, HRRH, RHHR, RHRH, RRHH also work. So you multiply by 6. That gives 96/625 = 0.1536, or 15.36%.
Re: A Math Question
The percentage of outcomes in which you get no rooster, assuming as you do that the ratio is effectively invariant, is (4/5)^4= 41%. The percentage of onerooster outcomes is (4/5)^3*1/5*4= 41% also. The remaining 18% of outcomes are divided up into 2, 3 and 4 rooster scenarios.
 RandyG
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Re: A Math Question
Would the same logic apply to ghoti?Woof wrote: ↑Tue Jun 30, 2020 5:39 pmThe percentage of outcomes in which you get no rooster, assuming as you do that the ratio is effectively invariant, is (4/5)^4= 41%. The percentage of onerooster outcomes is (4/5)^3*1/5*4= 41% also. The remaining 18% of outcomes are divided up into 2, 3 and 4 rooster scenarios.
 Rackme32
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Re: A Math Question
Are they laden or unladen?
Re: A Math Question
Go ghotiRandyG wrote: ↑Tue Jun 30, 2020 6:09 pmWould the same logic apply to ghoti?Woof wrote: ↑Tue Jun 30, 2020 5:39 pmThe percentage of outcomes in which you get no rooster, assuming as you do that the ratio is effectively invariant, is (4/5)^4= 41%. The percentage of onerooster outcomes is (4/5)^3*1/5*4= 41% also. The remaining 18% of outcomes are divided up into 2, 3 and 4 rooster scenarios.
Re: A Math Question
(Within minor rounding error) this is the correct answer and exactly the way to solve this problem. Well done.Volante wrote: ↑Tue Jun 30, 2020 3:19 pmTrying to dust the cobwebs off this part of my brain before working with numbers, but I'm concerned about your phrasing "that one of them is a rooster"triviawayne wrote: ↑Tue Jun 30, 2020 3:09 pmMy wife decided to buy chickens. She is hoping she doesn't end up with a rooster.
She said the lot of birds the store gets their supply from claims 80% are hens.
Since she bought 4 birds, I think the odds are 625:1 that one of them is a rooster.
Am I correct?
Is that the problem or "that at least one of them is a rooster" You could get up to four.
Maybe work the other way....
The chance of getting 4 hens, 80%*80%*80%*80% = 41%, so you have a 59% chance of getting at least one rooster?
Now, would you like to field our next question and try for the washerdryer?
Re: A Math Question
You, sir, listened to too many episodes of "Car Talk."
Re: A Math Question
I was going to make some remark about a sole rooster in the batch ending up a henpicked husband, but couldn't find a way to make it work.
I'm not the defending Jeopardy! champion. But I have played one on TV.
Re: A Math Question
Who cares about the math...I want to know why one can't sex a chicken?...Or is trying bound to get somebody in trouble these days...?...
Re: A Math Question
Actually, chicken sexing is a big thing. You don't want cockerels (which grow up to be roosters since they can't lay eggs), so common practice is to take the days old cockerels and put them through a shredder (yes, it's as awful as it sounds). This practice is already on the way out, but the ability to determine the sex in the egg would eliminate the need to do so.
 triviawayne
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Re: A Math Question
I really want to thank everyone for jumping in with the math.
My initial thought was either 41% or 59% by doing the 80*80*80*80 thing...but couldn't figure out which was the number I was looking for (we want to see zero roosters).
So far, it's looking like all hens...but time will tell.
My initial thought was either 41% or 59% by doing the 80*80*80*80 thing...but couldn't figure out which was the number I was looking for (we want to see zero roosters).
So far, it's looking like all hens...but time will tell.
Total game show career losings = $171,522
Re: A Math Question
There's an episode of American Dad that used this as a Bplot that I desperately wanted to reference in video form...but I couldn't find squat.alietr wrote: ↑Wed Jul 01, 2020 3:16 pmActually, chicken sexing is a big thing. You don't want cockerels (which grow up to be roosters since they can't lay eggs), so common practice is to take the days old cockerels and put them through a shredder (yes, it's as awful as it sounds). This practice is already on the way out, but the ability to determine the sex in the egg would eliminate the need to do so.
( https://en.wikipedia.org/wiki/Pulling_Double_Booty )
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Re: A Math Question
She wasn't a chicken (well, she sort of was), but we couldn't sex my parrot. Well, until we had her for about 10 years and she laid an unfertilized egg. Their important organs are all on the inside. Apparently, you can do it either via laparoscopy under anesthesia, or you can get a DNA test on feathers, and I'm not sure if that was commercially available in the late 90s, before she laid her egg.
Never really thought about it before, but she did have surgery to remove a benign tumor on her back when she was fairly young  at least 4 or 5 years before she laid the egg. I wonder if we could have done the laparoscopy then...although it probably would have been expensive, and just a "huh, interesting" kind of fact.