PEAX Equipment

Statistics!

VikingsGuy said:
So, are we helping you do your kid's math homework due to social distancing? ;)
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hahaha the quarantine is getting to everyone now! I figured I'd get maybe 1 or 2 responses back

haha! No, I'm trying to justify whether to apply as a party or individual for a cow hunt ha! To me if one 1 the two, or three draws it's a win and I go along. I wanted to see how drastic the odds changed when applying individually vs in a group.

Thanks @VikingsGuy imma formulate this into my excel SS and see if I'm able to comprehend it!
 
VikingsGuy said:
If we assume you meant 50 winning tickets out of 100 total tickets - which may not be what you meant but I am using the numbers we have at that moment:

If you then randomly receive 2 tickets you have the following odds:

24.75% chance of having 2 winning tickets
50.5% chance of having only 1 winning ticket
24.75% chance of having 0 winning tickets
In the aggregate you have a 75.25% chance of getting at least 1 winning ticket

When you pull your first winning ticket you have 50/100 odds of getting a winner, but when you pull your second ticket you have either 49/99 or 50/99 chance of pulling a winner with the second draw depending on the status of your first ticket (did it deplete winning tickets by one or losing tickets by one?).

There are four outcomes. WW, WL, LW, LL.

The odds of WW are .5 x 49/99 = .2475 (24.75%)
The odds of LL are .5 x 49/99 = .2475 (24.75%)
The odds of WL are .5 x 50/99 = .2525 (25.25%)
The odds of LW are .5 x 50/99 = .2525 (25.25%)
Because both WL and LW give you 1 winning ticket we add the odds 25.25% + 25.25% = 50.5%

The three ticket scenario would follow a similar approach but with 9 outcomes to be accounted for instead of 4
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Ok, still not comprehending....

If I buy 2 tickets (in lieu of 1 which gives me 50% odds) of the 100 and 50 are winners, my odds odds of a winning ticket only go up by 0.5%?
 
teej89 said:
hahaha the quarantine is getting to everyone now! I figured I'd get maybe 1 or 2 responses back

haha! No, I'm trying to justify whether to apply as a party or individual for a cow hunt ha! To me if one 1 the two, or three draws it's a win and I go along. I wanted to see how drastic the odds changed when applying individually vs in a group.

Thanks @VikingsGuy imma formulate this into my excel SS and see if I'm able to comprehend it!
Click to expand...
That's a lot trickier set of math than merely extrapolating from your example. And it depends on how the state handles party app issues such as PP averaging (or not) and "over draws" - meaning if you have 5 tags left does a 6 member party get excluded or included (will the state issue a 6th unplanned tag to complete the party?). If a state DOES add tags to allow for the full group then that boosts the party applicant odds by an amount dependent on how many tags are available to begin with (a very small uptick with many tags, a bigger relative uptick with small number of tags) - WY does this. But then states like NM go the opposite and drop party apps when insufficient tags remain - thereby having the opposite effect on odds. And there are other details about how states handle party apps that make this math super complex. In a broad sense, the odds for group apps are similar in large tag pools, but as tag pools get smaller state-specific rules may skew odds one way or the other.
 
teej89 said:
Ok, still not comprehending....

If I buy 2 tickets (in lieu of 1 which gives me 50% odds) of the 100 and 50 are winners, my odds odds of a winning ticket only go up by 0.5%?
Click to expand...

Your odds of getting a single winning ticket, but don't forget that getting two winning tickets is another outcome so your odds of having at least 1 winning ticket (1 winner or 2 winners) is up to 75.25%
 
VikingsGuy said:
That's a lot trickier set of math than merely extrapolating from your example. And it depends on how the state handles party app issues such as PP averaging (or not) and "over draws" - meaning if you have 5 tags left does a 6 member party get excluded or included (will the state issue a 6th unplanned tag to complete the party?). If a state DOES add tags to allow for the full group then that boosts the party applicant odds by an amount dependent on how many tags are available to begin with (a very small uptick with many tags, a bigger relative uptick with small number of tags) - WY does this. But then states like NM go the opposite and drop party apps when insufficient tags remain - thereby having the opposite effect on odds. And there are other details about how states handle party apps that make this math super complex. In a broad sense, the odds for group apps are similar in large tag pools, but as tag pools get smaller state-specific rules may skew odds one way or the other.
Click to expand...

yeah I figured, I was just doing some rough numbers for the fun of it.

I wasn't looking at it group wise, I was looking at it as if what if 1 person applies vs 2 vs 3. what are the different outcomes and what are the percentages, I was really dumbing it down.
 
VikingsGuy said:
Your odds of getting a single winning ticket, but don't forget that getting two winning tickets is another outcome so your odds of having at least 1 winning ticket (1 winner or 2 winners) is up to 75.25%
Click to expand...

Oh boy.

A single winning ticket out of the 2 is 75.25%?

So to get 75.25% I should be adding together the 50% (odds of first draw) plus the LW? Man I wish I paid attention in stats.

So is it correct that chance 1 of 2 tickets are winners is 75.25% and the chance they both win is 25.25% and chance they both lose is 25.25%?

How do I get to the 75.25% from looking at the 4 outcomes.
 
Shew weeee I'm going back to reading this 160 page research paper. Ouch guess I would have failed statistics.
 
teej89 said:
Oh boy.

A single winning ticket out of the 2 is 75.25%?

So to get 75.25% I should be adding together the 50% (odds of first draw) plus the LW? Man I wish I paid attention in stats.

So is it correct that chance 1 of 2 tickets are winners is 75.25% and the chance they both win is 25.25% and chance they both lose is 25.25%?

How do I get to the 75.25% from looking at the 4 outcomes.
Click to expand...

You have to calculate the odds of each outcome separately and then add them (there are really complex equations that get you there without manually working out each scenario, but that's way beyond what I can explain via an internet post). Go back to my explanation. You have WW, WL, LW and LL as the four draw outcomes. But since in your case you don't care about order of the results you add WL and LW together to get the solely 1 win odds. LL is the solely 0 win odds and WW is the solely 2 win odds. The odds of either 2 wins or 1 only win are the addition of WW + WL + LW.
 
VikingsGuy said:
You have to calculate the odds of each outcome separately and then add them (there are really complex equations that get you there without manually working out each scenario, but that's way beyond what I can explain via an internet post). Go back to my explanation. You have WW, WL, LW and LL as the four draw outcomes. But since in your case you don't care about order of the results you add WL and LW together to get the solely 1 win odds. LL is the solely 0 win odds and WW is the solely 2 win odds. The odds of either 2 wins or 1 only win are the addition of WW + WL + LW.
Click to expand...

Holy cow I think I got it!

Now let's see how I do when I try and work this out for 3 people, no hints I wanna try and tackle it.

Mind if I ask what do you do that you know this offhand?😂🤣
 
undergrad microbiology, grad school cellular/molecular biology, commercial R&D developed medical diagnostic assays
 
VikingsGuy said:
That's a lot trickier set of math than merely extrapolating from your example. And it depends on how the state handles party app issues such as PP averaging (or not) and "over draws" - meaning if you have 5 tags left does a 6 member party get excluded or included (will the state issue a 6th unplanned tag to complete the party?). If a state DOES add tags to allow for the full group then that boosts the party applicant odds by an amount dependent on how many tags are available to begin with (a very small uptick with many tags, a bigger relative uptick with small number of tags) - WY does this. But then states like NM go the opposite and drop party apps when insufficient tags remain - thereby having the opposite effect on odds. And there are other details about how states handle party apps that make this math super complex. In a broad sense, the odds for group apps are similar in large tag pools, but as tag pools get smaller state-specific rules may skew odds one way or the other.
Click to expand...

Not really on the topic of statistics, but,
I think Idaho drops the application due to not enough allotted tags left, then it goes to next person or party drawn. I don't think they add to the allotted tags. At least that's what I have been told.
 
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