stats help | Mathematics | Page 1

stoic hemlockBOT Sep 7, 2023, 2:44 AM

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golden jacinth Sep 7, 2023, 2:45 AM

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I keep getting 1/2, 5/16 or 5/36

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from different methods

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5/36 i multiply all outcomes (154) for each placement of 3 and then add. when 3 is first role (145) + when 3 is second roll (514) + when 3 is last roll (541)

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and then you divide that sum by 216

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so 20+20+20/216

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60/216

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which 5/36

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but then i did a binomail comp

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3 choose 1

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3!
!(3-1)! =3

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got the different probablities for each roll

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1/6 5/6 and 4/6

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multiplied them together and then multipled by 3 to account for different outcomes

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and got 5/16

golden jacinth Sep 7, 2023, 3:06 AM

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i just got that now

scenic thistle Sep 7, 2023, 3:09 AM

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@golden jacinthdo you know what the answer is supposed to be

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like do you have an answer key

golden jacinth Sep 7, 2023, 3:10 AM

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no it is a practice problem

scenic thistle Sep 7, 2023, 3:10 AM

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@golden jacinthOkay so I am NOT sure that this what i am about to say is correct

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so take it lightly

vapid fjord Sep 7, 2023, 3:12 AM

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golden jacinth

see your case #3
nothing is stopping 3 from being the first number

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what you can do is first pick where the 3 goes then think how many other numbers can fill the two other choices

golden jacinth Sep 7, 2023, 3:13 AM

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yes

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ok

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so 1/6 then 5/6 then 4/6

scenic thistle Sep 7, 2023, 3:13 AM

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i decided not to finish what I was writing since somebody who is more knowledgable came to help

vapid fjord Sep 7, 2023, 3:14 AM

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golden jacinth so 1/6 then 5/6 then 4/6

uhh count in like

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# of triplets

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like what you’re doing rn

golden jacinth Sep 7, 2023, 3:14 AM

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what?

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triplets?

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so 1/6 times 5/6 times 4/6

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times 3

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can u tell me which method is the right anwser

vapid fjord Sep 7, 2023, 3:16 AM

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so like

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I have 3 places to put the 3
_ _ _

golden jacinth Sep 7, 2023, 3:16 AM

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yes

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i understand that

vapid fjord Sep 7, 2023, 3:16 AM

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let’s just throw it in the middle

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_ 3 _

golden jacinth Sep 7, 2023, 3:16 AM

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ok

vapid fjord Sep 7, 2023, 3:17 AM

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now the first number can be any 5 of the other numbers

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and the last one any 4 of the remaining ones

golden jacinth Sep 7, 2023, 3:17 AM

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yes

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i get that

vapid fjord Sep 7, 2023, 3:17 AM

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and note that if you move the 3 anywhere else that’s still true

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so 5*4*3

golden jacinth Sep 7, 2023, 3:17 AM

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60

vapid fjord Sep 7, 2023, 3:17 AM

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well it’s probability

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you can do the last step

golden jacinth Sep 7, 2023, 3:18 AM

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oh so 60/216?

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SO 5/18 was CORRECT?

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thats the first way i did it

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wait are you sure?

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@vapid fjord does that account for the change

vapid fjord Sep 7, 2023, 3:21 AM

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oh what

vapid fjord Sep 7, 2023, 3:21 AM

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golden jacinth oh so 60/216?

well no youre given all 3 are already different

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this is condintional probability

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so its not 216 as denom

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unless im just readsing it wrong

golden jacinth Sep 7, 2023, 3:22 AM

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so 60/120

scenic thistle Sep 7, 2023, 3:23 AM

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That might sound really stupid but why is the following wrong:
Considering each dice lands on a different number
That would mean the first dice has 6 possible outcomes
the second (6-1) = 5 bcz one option is occupied by the first dice now
and the third 4 options

so 6+5+4 = 15 possible outcomes

we only need any of them to land on "3"

and considerng that all of them have the ability to do so can't we just do

3/15 = which is 20% chance?

or is that wrong?

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or why is it wrong

vapid fjord Sep 7, 2023, 3:23 AM

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uhh

scenic thistle Sep 7, 2023, 3:23 AM

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I feel like thats way too simple to be true

vapid fjord Sep 7, 2023, 3:23 AM

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it’s 6*5

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not 6+5

scenic thistle Sep 7, 2023, 3:23 AM

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why though

golden jacinth Sep 7, 2023, 3:23 AM

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golden jacinth so 60/120

wait so its 1/2?

vapid fjord Sep 7, 2023, 3:23 AM

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oh right you can easily complementary count

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kinda silly

vapid fjord Sep 7, 2023, 3:23 AM

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scenic thistle why though

draw a tree diagram

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you’ll quickly see it

golden jacinth Sep 7, 2023, 3:24 AM

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golden jacinth wait so its 1/2?

im confused still is it 1/2 or 5/18?

vapid fjord Sep 7, 2023, 3:24 AM

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golden jacinth wait so its 1/2?

pretty sure? but we can quickly check using complementary counting so find how many rolls we can omit a 3 from

vapid fjord Sep 7, 2023, 3:24 AM

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golden jacinth im confused still is it 1/2 or 5/18?

should be 1/2

golden jacinth Sep 7, 2023, 3:26 AM

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whats complentary counting?

vapid fjord Sep 7, 2023, 3:26 AM

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find all cases where there is no 3 among the dice

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Basically the opposite of what you want

golden jacinth Sep 7, 2023, 3:26 AM

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Oh

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hmm

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how do u write that out

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1/5?

vapid fjord Sep 7, 2023, 3:27 AM

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just forget a 3 exists from the dice

golden jacinth Sep 7, 2023, 3:27 AM

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yea thats why i said out of 5

vapid fjord Sep 7, 2023, 3:27 AM

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so how many numbers are in the first second third slots

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like triplets

golden jacinth Sep 7, 2023, 3:27 AM

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5 possiblities

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in each spot

vapid fjord Sep 7, 2023, 3:27 AM

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and then…

golden jacinth Sep 7, 2023, 3:27 AM

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so 5^3

vapid fjord Sep 7, 2023, 3:27 AM

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keep in mind the dice still need to be different

golden jacinth Sep 7, 2023, 3:27 AM

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oh shit so

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how do i

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repersent that

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543?

vapid fjord Sep 7, 2023, 3:28 AM

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yup

golden jacinth Sep 7, 2023, 3:28 AM

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5 x 4 x

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but didnt you do that to get the anwser

vapid fjord Sep 7, 2023, 3:28 AM

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and finally 1- probability of that happening is the probability of what we want

vapid fjord Sep 7, 2023, 3:29 AM

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golden jacinth but didnt you do that to get the anwser

yea

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but since the other was 1/2

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it makes sense

golden jacinth Sep 7, 2023, 3:50 AM

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golden jacinth 5*4*3?

Why Didn’t you start with 6

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Is it like this: the denominator is 6 times 5 times 4 cause that is counting the possibility of not selecting 3 and doing all possible outcomes. The numerator accounts for selecting 3 so that’s why it is 5 times 4 times 3 cause this is all total possible outcomes where you have selected 3

vapid fjord Sep 7, 2023, 4:46 AM

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golden jacinth Why Didn’t you start with 6

because we were counting how many combinations dotn include a 3

late vault Sep 7, 2023, 4:49 AM

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Answer should be 5/9

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120/216

vapid fjord Sep 7, 2023, 5:01 AM

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so its not 216 since its given that the rolls are different

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its IF all numbers are different

late vault Sep 7, 2023, 5:02 AM

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The dices are 3(666)

vapid fjord Sep 7, 2023, 5:06 AM

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oh i just realized...

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its just one three

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wait no

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its alright

vapid fjord Sep 7, 2023, 5:06 AM

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late vault The dices are 3(6*6*6)

yes im aware

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however we are given that the dice all have differnt numbers

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thus the denomiator is 6*5*4

golden jacinth Sep 7, 2023, 2:54 PM

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vapid fjord because we were counting how many combinations dotn include a 3

How does that get to the probability of getting 3

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If we don’t include 6?

vapid fjord Sep 7, 2023, 2:57 PM

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because we already picked a number to be the 3

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so then we can only have 12456 for the first one

golden jacinth Sep 7, 2023, 3:04 PM

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vapid fjord because we already picked a number to be the 3

Why do you do that to find the prob

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