help-0

[wanton junco]

2*x1x2 etc...

[floral pawn]

yep

so what i tried is once i got that, its the sum of all x_i*x_j = -1011

[wanton junco]

okay

[floral pawn]

i put it in a degree n polynomial

[wanton junco]

degree n polynomial ?

[floral pawn]

as the coefficient of x^(n-2)

like $x^n+a_1x^{n-1}-1011x^{n-2}+a_3x^{n-3}+...$

[ocean seal]

R31_

[floral pawn]

dont think itll give me anything useful though

[wanton junco]

wait waht was your reasoning for that ?

[floral pawn]

i let x_i for all i in {1,2,...,n} be roots of that polynomial

[wanton junco]

okay.. I dont seem to think of something that would follow along that path
but I think there's a much simpler method that you can follow

every number x_i lies between -1<x_i<1

[floral pawn]

what is it

[wanton junco]

therefore being multiplied by another such term would reduce it's value, meaning you'd have to add more terms to reach -1011

actually.. nvm I found a flaw in my method...

[lone heart]

@floral pawn Has your question been resolved?

[lone heart]

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[ripe magnet]

Okay question, I’m having a complete brain fart. So “find the magnitude and direction of the vector: ‘w’=u+v, and u=-4i-2j and v=3i+1j

Magnitude is 1.414
Direction is 45 degrees, no?

[ripe magnet]

Very easy but I’m just having L brain moment

Because -4i+3i=-1i
-2j+1j= -1j
Arctan that equals 45 degrees

Sqrt of -1^2+-1^2=1.414

Am I sound?

[gray isle]

Sqrt of -1^2+-1^2=1.414
missing parentheses
you can't blindly apply arctan

consider the position of w when you graph it

[ripe magnet]

Other than that I’m in the clear?

[gray isle]

try fixing your errors and see what you get

[ripe magnet]

I will

That’s all I needed to know honestly, much appreciated friend

.close

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[amber sage]

this is where i’m up to

i don’t know how to make it converge

[glass lichen]

Do you agree the integral doesn't converge b/c of the 1/(2x-1) part?

[amber sage]

yea i think

but the integral is divergent when c=0

wait no

so c should equal 0 right?

@glass lichen

oh never mind i think i read it wrong lmfao

.close

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[alpine sable]

find what x equals to

[graceful trench]

hello there

[alpine sable]

plug y into f(x)

f(y)=x

replace x by y

make it equal to x

just replace 3/2

then multiply both lhs and rhs by -1

and.... there we go

no

and this channel is occupied

so please find available channel

[graceful trench]

ok

[amber sage]

do you still need help

that’s the steps

swap x and y then solve for y

that’s the inverse function

@sonic gate

[glass lichen]

dont give answers.

[amber sage]

oh

hes offline bruh ;-;

[lone heart]

@sonic gate Has your question been resolved?

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[alpine sable]

Yeah absolutely no idea how to generalise this

I've never really done "generalising" past anything very simple

10c

[lone heart]

@alpine sable Has your question been resolved?

[alpine sable]

This is semi-urgent, I really should sleep

[tight locust]

Ok

[placid zinc]

Ignore the word "generalize". Just calculate part b again, but use m:n and p:q

Rather than 1:2 and 3:1

[alpine sable]

Okay I'll try

I can't really use x and y here

As I was doing previously

Before

Now

[lone heart]

@alpine sable Has your question been resolved?

[little drum]

wow this was the correct approach

If m/n and p/q is the ratio of wine/water, then

m/(m+n) x + p/(p+q)y = 500 was indeed correct

and x + y = 1000

so you need to figure x and y from these two equations

[lone heart]

@alpine sable Has your question been resolved?

[lone heart]

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[lone heart]

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[glad grove]

1 & 2

[tacit arch]

there are no numbers in your image

what have you tried?

[glad grove]

I mean the first 2 problems

It is supposed to be solved using eulers theorem

<@&286206848099549185>

<@&286206848099549185>

[tacit arch]

do you know euler's theorem?

did you try using chain rule?

[lone heart]

@glad grove Has your question been resolved?

[glad grove]

I tried giving them a variable and then tried partial differentiation

[tacit arch]

this just looks like a lot of derivative busywork. if you share your work someone can tell where you've made a mistake

maybe a start is all you need

calculate $\frac{\partial z}{\partial x}$

[ocean seal]

riemann

[lone heart]

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[astral solstice]

I want to prove convergenz

[echo socket]

Limit test?

[undone hinge]

bruder bist du eig student

[hasty elk]

or comparison test

[wanton junco]

maybe root test ?

[hasty elk]

so many tests

[karmic rapids]

ich würde dir empfehlen die chats auf deutsch zu halten c:

[wanton junco]

so many possibilities of failure

[astral solstice]

Alright 👍

[undone hinge]

versuche ich hahaha

[wanton junco]

personally I think root test is the simplest in this situation

[lone heart]

@astral solstice Has your question been resolved?

[little drum]

ratio test (@_@;)

[hasty elk]

why not go the whole hog, integral test

XD

or even better, Raabe's or Bertand's or Gauss' tests

maybe even Kummer's test

[wanton junco]

pcr test

[little drum]

maybe a mental health test

[hasty elk]

we're mathematicians

[pale kestrel]

Bound it with a geometric series, don't listen to these... people.

🤦

[little drum]

cos(nπ) is alternating 1, -1

[hasty elk]

like i said!

okay fine, the proper name is absolute comparison test, and you can use a geometric series to bound it

[astral solstice]

I know... that's my problem

So I just need to know how the denominator behaves?

[echo socket]

-1 <= cos <= 1

Use this

[astral solstice]

Leibniz?

[little drum]

$\sum_{n=0}^{\infty} \frac{\cos (n\pi)}{(\sqrt{2})^n} = \sum_{n=0}^{\infty} \qty(-\frac{1}{\sqrt{2}})^n$

[ocean seal]

Ansh

[astral solstice]

So I can use the Leibniz criteria?

[little drum]

the right side is a geometric series ._.

|ratio| < 1

[astral solstice]

yea

okay, so the solution is 0

xD

[little drum]

[astral solstice]

no wait

So it converges into $-\frac{1}{1-\frac{1}{\sqrt{2}}}$

[ocean seal]

Simplex

[little drum]

not quite. it should be +( ... )

[astral solstice]

thank you

.close

[lone heart]

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[peak owl]

Claim

[peak owl]

Just a quick question to make sure I'm not utterly dumb

By solution that just means where they intersect right?

[wary stream]

Yes

[peak owl]

Ok thanks lmao

.close

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[alpine sable]

is this correct? because wolfram alpha is giving me a different answer

[alpine sable]

wolfram is giving me this

[pale kestrel]

Why are you using degrees

[alpine sable]

uh because thats how we do it here

[hasty elk]

you should probably learn about radians even so, because like...the rest of the world uses radians

[alpine sable]

i will but for now i just wanna pass my finals 😂

[hasty elk]

especially when dealing with complex numbers

[pale kestrel]

I would not write this line

but ok, so far.

omfg

Why the heck do you think your answers are wrong

They're the same

[wanton junco]

-pi/2 => 270

[pale kestrel]

god that did my head in

[wanton junco]

pi/6 => 30

[alpine sable]

wait i thought pi was equal to 180

[wanton junco]

5pi/6= 150

[alpine sable]

wait what

[pale kestrel]

...................................

[alpine sable]

oh wow

[wanton junco]

these are conversions from radians to angles lol

[pale kestrel]

pi radians IS 180 degrees

[alpine sable]

i was doing 180/5 instead of 180/6

[pale kestrel]

christ

[alpine sable]

holy shit..

[wanton junco]

I was trying to figure this out as well lol

[alpine sable]

well thanks guys/gals

[wanton junco]

next time tho
you can just take your asnwers and apply ^3 to them

[alpine sable]

.close

[lone heart]

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[wanton junco]

and check for yourself if they fit
if they do then you're all good

[lone heart]

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[pale kestrel]

which substitutions have you tried

[fossil bluff]

is it just arcsin(y)

[buoyant kayak]

yes

[fossil bluff]

ok so i just did it bc i know thats the derivative of arcsin(x)

but the hint for the problem says substitute x=sin(t)

[pale kestrel]

go for it

[fossil bluff]

becomes sec(t) dx

[placid zinc]

Then the problem may be more about showing your work instead of knowing the answer

[fossil bluff]

i dont understand why that substitution is necessary nor where it leads to

[placid zinc]

Can get the answer without having to memorize it

x = sin(t)
dx = cos(t) dt

[fossil bluff]

ah

so you get \int_0^y dt

and t = arcsin(x)

[placid zinc]

(Also trig subs can get other integrals as well)

[fossil bluff]

what i said makes sense?

[placid zinc]

Yeah that's right

[pale kestrel]

u = f(x) substitution

ig this doesnt apply here rip

this time its x = f(t)

$$\int g(x)\dd x = \int f'(t)g(f(t))\dd t$$

[ocean seal]

Shuri2060

[pale kestrel]

So you have to spot your substitution will help which ig is hard/not always easy 🤔

[fossil bluff]

thanks people

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[lone heart]

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[alpine sable]

The result is wrong according to the book

I don’t see what I got wrong

[pale kestrel]

Can't see it.

Check with wolfram your answer vs original or something?

Or check with desmos

[naive valley]

What is the book's answer? Maybe it is equivalent.

[alpine sable]

the book’s answer is this

wouldn’t be surprised if it is equivalent

[pale kestrel]

sec^2

can be made into tan^2

using identity

[alpine sable]

didn’t know that

so i got it right?

[pale kestrel]

Check?

$$\cos^2+\sin^2=1$$

[naive valley]

sin^2 + cos^2 = 1. Divide both sides by cos^2 to get tan^2 + 1 = sec^2. The 1 gets included in the C.

[ocean seal]

Shuri2060

[pale kestrel]

You can create all pythag identities from this

[pale kestrel]

.

[alpine sable]

that’s very cool I didn’t know

thanks again

.close

[lone heart]

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[lone heart]

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[pale sable]

I'm not sure where to start, P_2 is the vector space of polynomials with degree 2

[lone heart]

@pale sable Has your question been resolved?

[tacit arch]

Check the definition?

https://en.wikipedia.org/wiki/Linear_subspace#Definition

[lone heart]

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[lone heart]

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[fresh relic]

Anyone know how to solve this?

[buoyant kayak]

point slope form, plug in info

[fresh relic]

y2-y1/x2-x1?

[buoyant kayak]

that's just how you find slope

use point slope form

[fresh relic]

what is point slope form?

[buoyant kayak]

$y-y_1=m(x-x_1)$

[ocean seal]

a disappointing son

[fresh relic]

so would it be 5-4=m(5-5)?

[buoyant kayak]

you may want to review algebra before you start doing calculus

[fresh relic]

I am already in calc

unfortunatel

precalc did not help me

<@&286206848099549185>

Please I need help I’m so stressed I have to get this before work and I’m so stressed please help

[lone heart]

@fresh relic Has your question been resolved?

[fresh relic]

<@&286206848099549185>

[daring coral]

what do you know of the relationship between the tangent line and derivatives?

[lone heart]

@fresh relic Has your question been resolved?

[lone heart]

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[carmine thistle]

Im sleep deprived because of this question.

[vocal hawk]

two possibilities

one blue then one red

or one red then one blue

[carmine thistle]

im mostly confused with 'is not replaced'

[vocal hawk]

it just means that when we take a ball

we don't return it back

[vocal hawk]

so for this case

for a blue ball

it's 4/9

then for a red one after this

5/8

8 cuz it's now 8 balls instead of 9

[carmine thistle]

so do i do 4/9 x 5/8

[vocal hawk]

yes

[carmine thistle]

to get answer

[vocal hawk]

one posibility

second one

is the same actually

[vocal hawk]

this

5/9 * 4/8

then add them

[carmine thistle]

i tried this

didn't work

ill try add

i got unlimited tries

[vocal hawk]

you have two possibilites

so it's 5/18 * 2

[carmine thistle]

i dont think this one works

[vocal hawk]

why?

the possibility of getting a red one is 5/9

then to get a blue one after it

[carmine thistle]

5/9 + 4/8 = 19/18

[vocal hawk]

4/8

mulitpication

[carmine thistle]

oh

[carmine thistle]

.

[vocal hawk]

yes

[carmine thistle]

was wrong

[vocal hawk]

you did one possibility

[carmine thistle]

oh

[viral cairn]

b/c you take out a marble if it asked you to return it would be * the same value

[vocal hawk]

each one is 5/18

[carmine thistle]

i dont understand this

[vocal hawk]

so 5/18 + 5/18

so 10/18

[carmine thistle]

simplifies to 5/9

[vocal hawk]

yeah

[carmine thistle]

im really confused

this homework

makes me sleep deprived

its 2 am

[vocal hawk]

chill

and think about it

you have two colors

red and blue

you need to take two balls

and get different colors

so you might get blue then red

OR

red then blue

right?

[carmine thistle]

yes

[viral cairn]

4/18*5/17

[carmine thistle]

i got this now

exactly

1

red

so

5/8

right

[vocal hawk]

was 5/9 right?

[carmine thistle]

yeah

[vocal hawk]

ok good

[viral cairn]

I didnt do the calculations

[ruby summit]

Remember #rules

[carmine thistle]

what about this one

any ideas

[carmine thistle]

wdym

???

[ruby summit]

Just reminding caution to the helpers

[carmine thistle]

you are mod?

[ruby summit]

No

[carmine thistle]

is mini mod allowed

[vocal hawk]

he's just reminding us to be helpful

[ruby summit]

I just want to make sure everyone is following the rules

[carmine thistle]

ok

[vocal hawk]

and to explain stuff

[carmine thistle]

okk

[vocal hawk]

not give out answers

[carmine thistle]

alright

[viral cairn]

you will prob have to use cases

[carmine thistle]

for this is it 4/17

because

[ruby summit]

Sometimes everyone needs a reminder, I know I like one... I want to make sure no one breaks a #rules and then gets banned

[carmine thistle]

not replaced

[carmine thistle]

ok

[vocal hawk]

for thsi one

it's the same

you are taking two balls

not one

[carmine thistle]

oh

[vocal hawk]

so what is the possibility of getting 1 red out of two times?

[ruby summit]

The cases both involve dividing by 8 and 7 therefore that must be the denominator?

[carmine thistle]

1/2

right

[vocal hawk]

no

[carmine thistle]

idek

[vocal hawk]

think about it

you need 1 red

how can that happen?

[carmine thistle]

10/18?

because

5/9

x

2

[ruby summit]

Seperate it out into two times

[carmine thistle]

idek

i lost

like

6 months

of school

im 15

[ruby summit]

What is the probability that you get a red ball the first time...

[carmine thistle]

and dont know

[viral cairn]

it involves logic

[carmine thistle]

yeah

[carmine thistle]

5/8

[vocal hawk]

stop guessing numbers

and chill

and think

[carmine thistle]

first time

[vocal hawk]

how can you get 1 red ball

[carmine thistle]

oh

[vocal hawk]

if you are taking two balls

[ruby summit]

Wait what?

[carmine thistle]

i am confused

[ruby summit]

Oh, I get what you're are getting at

[vocal hawk]

ok first time you pick a ball

[carmine thistle]

yes

[vocal hawk]

you can get what?

[carmine thistle]

red

or

blue

[vocal hawk]

good

now if you get red

what can you get after it

[carmine thistle]

blue

or

red

[vocal hawk]

good

same thing if you got blue first

so red -> red
or red -> blue
or blue -> blue
or blue -> red

right?

[carmine thistle]

yes

[vocal hawk]

when do you get exactly one red ball

[carmine thistle]

1/4

[vocal hawk]

look again

[carmine thistle]

first time

[ruby summit]

R is the event of picking red, B is the event of picking blue R --> R or B, or B --> R or B

[vocal hawk]

it's the second and fourth cases

red then blue OR blue then red

are you following?

[carmine thistle]

yes

[vocal hawk]

ok

now calculate each of these two cases

and add them up

first case

red then blue

try to calculate it

[carmine thistle]

5/8 + 3/8

right?

[vocal hawk]

no

it's dependent

so first 5/8

the ball is now gone

so we have 7 balls

so 3/7

and you multiply

5/8 * 3/7

are you following? any issues here?

[carmine thistle]

15/56

5/8 x 3/7 = 15/56

then double right?

[vocal hawk]

yeah double for the other case

[carmine thistle]

15/56 + 15/56

30/56

[vocal hawk]

that is blue then red

[carmine thistle]

this is so confusing

[vocal hawk]

which part?

[carmine thistle]

all of it

apart from finding

3/7

5/8

oh

30/56

=

15/28

so thats answer

[ruby summit]

That is not what I got

[carmine thistle]

i got that

its right

[ruby summit]

Okay

[carmine thistle]

so its 3/7 x 5/8

15/56

15/56 + 15/56

[viral cairn]

what did you get bman

ill compare to you

[ocean seal]

Bman

[carmine thistle]

15/28 was right

idk how

this was the question

[ruby summit]

What did you get?

[carmine thistle]

i got a new question but 'getting exactly 1 blue' everything else the same

would answer be the same

i mean

at least

1 blue

not

exactly

[vocal hawk]

this is different

at least 1 blue

now do the same steps

think

[ruby summit]

It is way easier

[carmine thistle]

red red

red blue

blue blue

blue red

[vocal hawk]

blue red last one

[carmine thistle]

ok

[vocal hawk]

great

which ones are at least 1 blue?

which cases?

[carmine thistle]

3

of them

[vocal hawk]

yes

[carmine thistle]

all but not red red

[vocal hawk]

2,3,4

good

[carmine thistle]

yes

[vocal hawk]

not calculate each of these three cases

[ruby summit]

So what are the chances of not getting red and a red

[vocal hawk]

oh

yah

you can calculate the chance of not getting red and red instead

[ruby summit]

1 - probability of getting red and red

[vocal hawk]

instead of calculating 3 cases

[carmine thistle]

alright

[vocal hawk]

makes things easier

[ruby summit]

What I said

[carmine thistle]

alright

so

prob of red red

=

5/8

x

5/8

right

[vocal hawk]

no

[ruby summit]

no

[vocal hawk]

remember

we don't put the ball back the second time

5/8

x

what?

[carmine thistle]

hm

3/7

5/7*

[ruby summit]

Close

[carmine thistle]

oh wait

i got to decrease 5

so 4/7

[vocal hawk]

yuppp

[ruby summit]

Correct!

[vocal hawk]

see

it's logical

[carmine thistle]

5/8 x 4/7 = 5/14

[vocal hawk]

you just need to think

yeah

[carmine thistle]

let me check

[vocal hawk]

now

wait

[ruby summit]

No

[vocal hawk]

this is getting red red

remember

[carmine thistle]

oh alr

1- 5/14

[vocal hawk]

yess

[ruby summit]

Correct!

[carmine thistle]

9/14

[ruby summit]

Yes!

[vocal hawk]

not getting red red is 1-5/14

yup

good job

[carmine thistle]

ty

[vocal hawk]

np

[carmine thistle]

now i got this

but

3 colours

it works same

?

[vocal hawk]

same

but more cases

[ruby summit]

depends....

[ruby summit]

yes.

[carmine thistle]

this is the question

[ruby summit]

Yes it is the same process

[carmine thistle]

/12

so

4/12 = B

3/12 = R

5/12 = G

3/11

= b

???

[vocal hawk]

this one has more cases

you first need to write down the cases

[carmine thistle]

Blue Blue Blue

Red Red Red

[vocal hawk]

b - b -r
b - b -g
b - r -b
b -g -b
r - b - b
g - b -b
b - b -b

[carmine thistle]

o

k

[vocal hawk]

wrote them for you

[carmine thistle]

tysm

[vocal hawk]

remember

wait

two balls only is drawn

[carmine thistle]

oh

[vocal hawk]

nvm

you draw two balls

what are the cases of getting two blues ?

[carmine thistle]

7

times

[vocal hawk]

no

think again

you pick two times

and you need two blues

how can you do that?

[carmine thistle]

once

[vocal hawk]

how many different way?

yes

blue then blue

that's it

calculate it

[carmine thistle]

1/

bb

br

bg

rg

[vocal hawk]

no here you don't need to write all the cases

you know it's only one case

[carmine thistle]

so i write 1

[vocal hawk]

there's 1 case

b - b

[carmine thistle]

yeah

[vocal hawk]

what is the probability of this case

[carmine thistle]

idk

[vocal hawk]

what is the possibility of getting a blue ball the first time?

[carmine thistle]

1/3

[vocal hawk]

4/12 yeah

what is the probability to get a blue ball the second time

[carmine thistle]

once

[vocal hawk]

probability

not how many cases

[carmine thistle]

1/4

[vocal hawk]

no

we took a blue one the first time remember ?

it's not replaced

[carmine thistle]

so

out of

11

[vocal hawk]

yup

out of 11 now

how many blue?

[carmine thistle]

1

[vocal hawk]

no

[carmine thistle]

4

[vocal hawk]

no

[carmine thistle]

4 blue

oh

3

[vocal hawk]

it was 4 blue the first time

now it's 3

yes

so

[carmine thistle]

ok

so

[vocal hawk]

4/12

x

[carmine thistle]

3/11

[vocal hawk]

yup

[carmine thistle]

so 1/11

yess

[vocal hawk]

yeah

[carmine thistle]

for triple ones

how do i do exact

[vocal hawk]

always try to imagine it

and think about the cases

but if there's only one case

you don't need to write it all down

[carmine thistle]

ok

[vocal hawk]

only write the cases that you want to calculate

[carmine thistle]

alright

im gonna try do this one

i mean

not that

diff

thats old one

[vocal hawk]

yeah that's the previous one

[vocal hawk]

ok

try to do this

[carmine thistle]

5/12

x

7/11

=

35/132

then

lemme try

it

[vocal hawk]

how did you get 7/11?

[carmine thistle]

i got

i mean

8/11

wait

no

6/11

because

one goes

[vocal hawk]

first know how many cases are there

[carmine thistle]

2

[vocal hawk]

which are?

write the cases that you need

[carmine thistle]

green

exactly 1 green

5/12 greens

probability

for

first green

3+4+5

=12

1-5/12

=

7/12

7/11

5/12

x

7/11

=35/132

[vocal hawk]

I don't think that's right

write down the cases first, you are picking two balls, how can you get 1 green exactly?

[carmine thistle]

wait let me send question

again

[vocal hawk]

ok

you pick two times right?

[carmine thistle]

yeah

because

another marble

[vocal hawk]

you want 1 green exactly

how can this happen ? how many cases?

[carmine thistle]

i dont understand

how many cases

[vocal hawk]

I mean you can get b-g

or r-g

like that

[carmine thistle]

yes

[vocal hawk]

there are two more

[carmine thistle]

gb

gr

[vocal hawk]

yes

so 4 cases

bg
rg
gb
gr

there are other cases

but we don't need them

we don't care about them

bb for example

we don't care

[carmine thistle]

ok

[vocal hawk]

so write down only the ones you need

[carmine thistle]

ok

[vocal hawk]

then calculate each one of these 4

[carmine thistle]

5/12 x 4/12

5/12 x 3/12

[vocal hawk]

no

remember

the ball is gone the second time

[carmine thistle]

oh

so only once

wait a sec

[vocal hawk]

I mean

[carmine thistle]

watch

7/12 x 5/11

= 35/132

35/132 + 35/132

=

[vocal hawk]

why 7?

[carmine thistle]

70/132

=

35/66

[carmine thistle]

because

7 remains

in probability

5/12 = 5/11

[vocal hawk]

oh right

[carmine thistle]

because not replaced

right?

[vocal hawk]

no wait

[carmine thistle]

ok

[vocal hawk]

5/12

5/12 x 7/11

first time

[carmine thistle]

same

answer

[vocal hawk]

yeah same

same answer

[carmine thistle]

yes

[vocal hawk]

but different logic

[carmine thistle]

5/12 x 7/11

5/11 x 7/12

[vocal hawk]

yup

yeah I didn't think of this way

but it's right

and better

[carmine thistle]

but i think in exam

your way is better

because working out marks

[vocal hawk]

it's all the same

use whatever you feel better

but most importantly make sure you understand them

[carmine thistle]

yes

i just got same question but

getting the 2 same colour

There is a bag filled with 3 blue, 4 red and 5 green marbles.
A marble is taken at random from the bag, the colour is noted and then it is not replaced.
Another marble is taken at random.
What is the probability of getting 2 the same colour?

there is

3

cases

bb

[vocal hawk]

yes

[carmine thistle]

rr

gg

[vocal hawk]

good

very good

calcualate them then add

[carmine thistle]

bb = 3/12 x 2/11 = 1/22

rr = 4/12 x 3/11 = 1/11

[vocal hawk]

not replaced

don't forget

3/12 x 2/11

[carmine thistle]

gg = 5/12 x 4/11 = 5/33

[vocal hawk]

yes

[vocal hawk]

also here

4/12 x

yup

right

don't forget this

[carmine thistle]

1/22

1/11

5/33

=

[vocal hawk]

yeah

[carmine thistle]

19/66

There is a bag filled with 4 blue, 3 red and 5 green marbles.
A marble is taken at random from the bag, the colour is noted and then it is not replaced.
Another marble is taken at random.
What is the probability of getting 2 different colours?

so

br

bg

[vocal hawk]

wait

[carmine thistle]

rg

[vocal hawk]

you are doing it right

but

there's an easier way

[carmine thistle]

ok

the same colour

1-

same colour

right?

[vocal hawk]

yess

[carmine thistle]

bb

gg

rr

[vocal hawk]

we just did it

[carmine thistle]

this different numbers

thats why

[vocal hawk]

1-same color

we did same color

[carmine thistle]

There is a bag filled with 4 blue, 3 red and 5 green marbles.
A marble is taken at random from the bag, the colour is noted and then it is not replaced.
Another marble is taken at random.
What is the probability of getting 2 different colours?

yes

ok

[vocal hawk]

this

[carmine thistle]

so

1-19/66

[vocal hawk]

yes

[carmine thistle]

47/66

[vocal hawk]

getting 2 different colors = not getting same colors == 1-getting same colors

[carmine thistle]

yes its right

yes

do you know how to do this

it took me 1hr

and i got it wrong

its an impossible

question

[vocal hawk]

you need to use this formula

probabilty of A given B

[carmine thistle]

does middle count as

A

and middle count as B

so

[vocal hawk]

middle count

so train is 9

cycle is 14

probability of A given B

= p(A AND B)/p(B)

A is cycle

B is Train

[carmine thistle]

it says

B = Bicycle

T = Train

idk

[vocal hawk]

yeah yeah my bad

[carmine thistle]

same thing

tho

a = b

b = t

[vocal hawk]

probability of

no no

dont' confuse it

[carmine thistle]

a b = b t

i mean

[vocal hawk]

well ok

you can do it

but use the formula

[carmine thistle]

ok

[vocal hawk]

A and B

is middle

so p(A and B) here is 3

[carmine thistle]

3/6

3/9*

[vocal hawk]

yes

3/9

[carmine thistle]

cause middle counts

[vocal hawk]

yup

[carmine thistle]

ok

[vocal hawk]

I think

this is true

[carmine thistle]

yes

its right

do you know

mutually exclusive

[vocal hawk]

yes

[carmine thistle]

i dont know what it means

teacher never taught us it

[vocal hawk]

mutually exclusive

means

can't be both

so

B and T

no one can do both

it's mutually exclusive

T and W

can be both

not mutually exclusive

B and W

can't be both

mutually exclusive

[carmine thistle]

wdym by

cant be both

[vocal hawk]

I mean

check the graph

W is walk

T is train

there are 7 people

who do walk and train

right?

but no one is doing bicycle and train

[carmine thistle]

oh yeah

[vocal hawk]

bicycle and train can't occur both at the same time

B and T are mutually exclusive

get it?

[carmine thistle]

so this is also logical

[vocal hawk]

yes

[carmine thistle]

i add up all values

right

i get 25

4/25