## monroe17 3 years ago 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)

1. TuringTest

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

2. monroe17

3

3. monroe17

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

4. monroe17

2 outcomes for each right?

5. 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

6. monroe17

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

7. TuringTest

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

8. TuringTest

|dw:1339812046337:dw|

9. monroe17

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?

10. monroe17

OHH okay.

11. monroe17

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

12. monroe17

and 2 ways for the second question?

13. TuringTest

no and yes respectively

14. 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

15. TuringTest

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

16. monroe17

|dw:1339812287194:dw| this?

17. 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

18. monroe17

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

19. monroe17

BG,BT,TG

20. TuringTest

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

21. monroe17

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

22. monroe17

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

23. 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?

24. TuringTest

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

25. TuringTest

what is the exact wording of the question?

26. monroe17

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?

27. 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?

28. monroe17

BT?

29. 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?

30. monroe17

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

31. 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?

32. monroe17

OH HAHA.. sorry. 6 ways.

33. monroe17

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

34. TuringTest

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

35. TuringTest

|dw:1339813592285:dw|

36. TuringTest

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

37. monroe17

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?

38. TuringTest

exactly :)

39. monroe17

Wow, thanks so much:D

40. TuringTest

very welcome, see ya!