Suppose you have socks loose in a drawer. You have a black sock, a gray sock and a tan sock. How many outcomes are there for selecting 2 socks?
a. make a tree diagram to model the selection of 2 socks WITHOUT replacement. (That is, you keep the sock out of the drawer and there is now one less sock to choose from)

- anonymous

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- TuringTest

to make a tree diagram you draw one line for each possible choice
how many possible outcomes are there for the first sock?

- anonymous

3

- anonymous

I'm not even sure how to solve it first of all.

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## More answers

- anonymous

2 outcomes for each right?

- TuringTest

the question you posted just asks for the diagram, so just draw a line for each possible sock
label each one b, g, or t

- anonymous

|dw:1339811932001:dw|
like that or different?

- TuringTest

no, they are all supposed to originate from the same point

- TuringTest

|dw:1339812046337:dw|

- anonymous

I also have to find out: how many ways can you select 2 socks without replacement? and How many ways can you get a black and a tan sock?

- anonymous

OHH okay.

- anonymous

For the first question isn't it only one way without replacement?

- anonymous

and 2 ways for the second question?

- TuringTest

no and yes respectively

- TuringTest

there are two ways for the next trial to occur. can you draw in the lines that would represent the next branches of the tree
it will be the same as before, but with two branches for each possibility

- TuringTest

try to draw it in with the "reply using drawing" feature

- anonymous

|dw:1339812287194:dw|
this?

- TuringTest

yes, very nice
note that you could have hit the upper-right corner of my drawing to avoid drawing the whole thing over again
so how many distinct pairs are there? you can count them
watch out for duplicates though. remember that bt=tb
the order of pulling out the socks does not matter

- anonymous

ohh lol! thanks for the note.
Uhm, there are 3 pairs?

- anonymous

BG,BT,TG

- TuringTest

|dw:1339812688135:dw|yep, 3 distinct pairs :)

- anonymous

So there are 3 ways to select 2 socks without replacement?

- anonymous

and 2 ways to get a Black and Tan sock.. TB and BT?

- TuringTest

well the difficulty comes in the wording
what do you think they are asking you?
is a black then tan different from a tan then black?

- TuringTest

if they are different, there are 6 possibilities as you can see
if all that matters are the possible pairs, then 3

- TuringTest

what is the exact wording of the question?

- anonymous

Suppose you have socks loose in a drawer. You have a black sock, a gray sock, and a tan sock. How many outcomes are there for selecting 2 socks?
a. Make a tree diagram to model the selection of 2 socks WITHOUT REPLACEMENT. (That is, you keep the sock out of the drawer and there is now one less sock to choose from)
b. How many ways can you select 2 socks without replacement?
c. How many ways can you get a black and a tan sock?

- TuringTest

ok, since they ask "how many ways you can get a black and tan sock" that means to me that they consider bt distinct from tb (the order you pull them out seems to matter)
so then what is b?

- anonymous

BT?

- TuringTest

no I mean the answer to part b)
what is it if they consider pulling out a black then green \(different\) from green then black?

- anonymous

Then the answer is two ways; BT and TB. Right? Since they're considering them different.

- TuringTest

that would be the answer to part c
but what about the total number of ways to pull out the socks? our earlier answer, 3, was based on the idea that BT and TB are the same
but since we now think they are different, what is our new answer?

- anonymous

OH HAHA.. sorry.
6 ways.

- anonymous

wait 6 ways, without replacement? What does it mean by without replacement though?

- TuringTest

yes, otherwise it would be 3x3=9 ways (think about what the tree diagram would look like to see why)

- TuringTest

|dw:1339813592285:dw|

- TuringTest

that would be with replacement, which would allow us to pull, say, the black sock out twice

- anonymous

ohhhh gotcha! So my tree diagram is correct from the above picture I drew and the answer to part B is 6 ways and the answer to part C is two ways BT and TB?

- TuringTest

exactly :)

- anonymous

Wow, thanks so much:D

- TuringTest

very welcome, see ya!

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