Question

@perl

Answer 1

1 card white both sides, 1 black both sides, 1 white one side black one side, u close ur eyes, pick one card at random, open your eyes, and see it's a white side. what's the chance that the other side is also white

Answer 2

are you serious?

Answer 3

shhhhh

Answer 4

ok one sec

Answer 5

can you give me a minute

Answer 6

Ya sure

Answer 7

@dan815

Answer 8

dan815
okay look
its
ww,bb,wb
ww,bb,bw 2 cases 50% chance
for case 1
2/3 chance u pick w, and 1/2 chance u get white
for case 2
1/3 chance u pick w, and 100% chance u get white
so
2/3*1/2 + 1/3*1 = 2/3 which is COMPLEETELLLYY WRONNG!!

lol...this is what he sent me.

Answer 9

i thohgut i sent that to swiss lol

Answer 10

smh

Answer 11

but ya LOOK
there are 2 cases in total
w ,w ,b and b , w ,b
there are a total of 3 ws
for 2 of the 2s there is 1/2 change it is white on bac
and 1 w there is 100% chance

Answer 12

therefore 2/3*1/2 +1/3*1 = 2/3

Answer 13

I HAVE SOLVED IT

Answer 14

this question 100% undestood it is mine

Answer 15

BAHAHAHAHAHAHAHAHAHHA

Answer 16

Take ur meds pls -.-

Answer 17

it should be 1/2 i think

Answer 18

ughhh thats what i thought .... but maybe i was oversimplifying

Answer 19

okay i though so at first 2, but think about it ganeshie u arent picking white haof the time u are more like to pick a white when its black on the other side

Answer 20

P(ww | w) = P(ww and w)/P(w)

Answer 21

there are 2 cases
one where white is facing him and black is facing him

Answer 22

when white is facing him he has a higher hance of picking white, which lowers it being white on the back

Answer 23

if u were to do a computer simulation

Answer 24

`ww,bb,wb`

since you know that one side is w, the sample space shrinks to
`ww, wb`

Answer 25

or just ww

Answer 26

since the b cud be facing other way to begin with

Answer 27

# of outcomes in favor = 1
total # of outcomes = 2

take the ratio for probability

Answer 28

it should be as simple as that right ?

Answer 29

theres more to it ummm

Answer 30

if u thnk about a computer program

Answer 31

when its w w b , it will pick w more often

Answer 32

when its b b w, i will pick white only 1/3 of the time

Answer 33

dan, please...

Answer 34

-.-

Answer 35

stick to modern physics :)

Answer 36

since you know one face is white already, you can remove "bb" and update ur sample space

Answer 37

but ya LOOK there are 2 cases in total
w ,w ,b and b , w ,b
there are a total of 3 ws for 2 of them ws there is 1/2 chance it is white on bac
and 1 w there is 100% chance

therefore 2/3*1/2 +1/3*1 = 2/3

Answer 38

but the way he arrive at white is different

Answer 39

you have 3 cards to start with, yes ?

Answer 40

like 2/3 of the time it is ww,wb
but 1/3 of the tiem its just ww case he picks a w

Answer 41

u cannot say that wb still exists in the sample space

Answer 42

yeah

Answer 43

the knowledge of one face being "w" allows you to remove the possibility "bb" yes ?

Answer 44

yep

Answer 45

we can ignore all the past and look at our new sample space

Answer 46

it has two outcomes now :

ww, wb

Answer 47

ehh

Answer 48

only one is in ur favor, isn't your particle filter works the same way ?

Answer 49

no theres moree to it i think

Answer 50

here we go with your "there's more to it" LAUGHING OUT LOUD
there's nothing more!

Answer 51

why -.-

Answer 52

hahaha Dan sees the world in a 3D format

Answer 53

it doesnt make senseee theres gotta be more

Answer 54

then figure out what it is then come back to us with what you figured out

Answer 55

if i was holding a white card, id be thinking, okay if i am holding a white card, then there is something fishy here

Answer 56

there is a higher chance of me holding a white card when they are both facing white

Answer 57

you're onto something I must have

Answer 58

and there is a less chance of me holding a white card when only 1 is facing white

Answer 59

Canadian kush?

Answer 60

hmmmm

Answer 61

right, when u are holding white, 2/3 of the time its with its w w b
so that means 1/2 for that case
but 1/3 of the time it is w b b, in this case 100% chance its white

Answer 62

u see what i mean ganeshie?

Answer 63

why isnt it like this?

Answer 64

I CAN PROVE IT!

Answer 65

yes, but you're not using the information that one of the cards is white

Answer 66

i cann proove i!!

Answer 67

i think you're calculating P(ww)

the question wants P(ww|w)

Answer 68

make 50 tuple sets on program

Answer 69

[(b,b),(w,w),(w,b)]<---- 50 of this
[(b,b),(w,w),(b,w)]<---- 50 of this too
Lets randomly pick
index 1:3 and index 1 of each tupple

Answer 70

everytime its white , lets check index 2 of the same tuple

Answer 71

and see how many times we get white!!

Answer 72

I see you get ww more times

Answer 73

we can just eliminate bb since its useless

Answer 74

Ya dannnn.... You already picked a white

Answer 75

idk you have confused me already :o

Answer 76

so u are only left with
ww wb
ww, bw when u eliminate bb from cases

Answer 77

and u know the bw case is excluded when u get it

Answer 78

ww, wb,ww

Answer 79

I should give dan a medal for confusing people

Answer 80

so 2/3 of the time its ww

Answer 81

lol

Answer 82

ty for ur medal i take all medals

Answer 83

i need 500 more for future MATH PROFESSOR

Answer 84

dan, your arithmetic sucked.
https://www.khanacademy.org/math/probability/independent-dependent-probability/basic_probability/v/basic-probability

Answer 85

LOL why are u sending me to prob video

Answer 86

because that is what you need

Answer 87

bahahha

Answer 88

There are six possibilities, all equally likely.

- ww card with white "A" up / white "B" down
- ww card with white "B" up / white "A" down
- bw card with the white up / black down

- bw card with the black up / white down
- bb card with black "A" up / black "B" down
- bb card with black "B" up / black "A" down

Note that we have white up, so we can eliminate the last three possibilities. But each of the other three possibilities are all still equally likely. And there are two possibilities where other side is also white, thus the probability is \(\boxed{2/3}\)

Answer 89

hmmm gotcha ;(

Answer 90

Looks like @dan815 doesn't need to watch video at all :P

@nincompoop

Answer 91

What do you think of my solution? @ganeshie8

Answer 92

i love u micah <3

Answer 93

Nice :) I see what dan was saying earlier now @micahwood50

Answer 94

he still needs to watch the video; it doesn't hurt anyone to learn probability properly