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monroe17

  • 2 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)

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  1. TuringTest
    • 2 years ago
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    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
    • 2 years ago
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    3

  3. monroe17
    • 2 years ago
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    I'm not even sure how to solve it first of all.

  4. monroe17
    • 2 years ago
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    2 outcomes for each right?

  5. TuringTest
    • 2 years ago
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    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
    • 2 years ago
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    |dw:1339811932001:dw| like that or different?

  7. TuringTest
    • 2 years ago
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    no, they are all supposed to originate from the same point

  8. TuringTest
    • 2 years ago
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    |dw:1339812046337:dw|

  9. monroe17
    • 2 years ago
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    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
    • 2 years ago
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    OHH okay.

  11. monroe17
    • 2 years ago
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    For the first question isn't it only one way without replacement?

  12. monroe17
    • 2 years ago
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    and 2 ways for the second question?

  13. TuringTest
    • 2 years ago
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    no and yes respectively

  14. TuringTest
    • 2 years ago
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    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
    • 2 years ago
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    try to draw it in with the "reply using drawing" feature

  16. monroe17
    • 2 years ago
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    |dw:1339812287194:dw| this?

  17. TuringTest
    • 2 years ago
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    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
    • 2 years ago
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    ohh lol! thanks for the note. Uhm, there are 3 pairs?

  19. monroe17
    • 2 years ago
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    BG,BT,TG

  20. TuringTest
    • 2 years ago
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    |dw:1339812688135:dw|yep, 3 distinct pairs :)

  21. monroe17
    • 2 years ago
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    So there are 3 ways to select 2 socks without replacement?

  22. monroe17
    • 2 years ago
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    and 2 ways to get a Black and Tan sock.. TB and BT?

  23. TuringTest
    • 2 years ago
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    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
    • 2 years ago
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    if they are different, there are 6 possibilities as you can see if all that matters are the possible pairs, then 3

  25. TuringTest
    • 2 years ago
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    what is the exact wording of the question?

  26. monroe17
    • 2 years ago
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    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
    • 2 years ago
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    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
    • 2 years ago
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    BT?

  29. TuringTest
    • 2 years ago
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    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
    • 2 years ago
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    Then the answer is two ways; BT and TB. Right? Since they're considering them different.

  31. TuringTest
    • 2 years ago
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    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
    • 2 years ago
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    OH HAHA.. sorry. 6 ways.

  33. monroe17
    • 2 years ago
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    wait 6 ways, without replacement? What does it mean by without replacement though?

  34. TuringTest
    • 2 years ago
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    yes, otherwise it would be 3x3=9 ways (think about what the tree diagram would look like to see why)

  35. TuringTest
    • 2 years ago
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    |dw:1339813592285:dw|

  36. TuringTest
    • 2 years ago
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    that would be with replacement, which would allow us to pull, say, the black sock out twice

  37. monroe17
    • 2 years ago
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    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
    • 2 years ago
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    exactly :)

  39. monroe17
    • 2 years ago
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    Wow, thanks so much:D

  40. TuringTest
    • 2 years ago
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    very welcome, see ya!

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