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Math Help - Probability - Matching terms and definitions question

  1. #1
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    Probability - Matching terms and definitions question

    I wondered whether I was on the right track with regard to the following question:


    A student has to match three terms that she has never seen before with their definitions. If she guesses, what is the probability of her

    1. Getting all three correct?
    2. Getting none correct?
    3. Getting exactly one correct?
    4. Getting exactly two correct?

    What assumptions did you make? Do they seem reasonable?
    Hint: List the sample space.

    Using numbers to represent definitions and letters to represent terms, I think the sample space should be as follows:

    A1 B1 C1
    A2 B2 C2
    A3 B3 C3

    If we say that A3, B3 and C3 are correct, these are my tentative answers:

    probability of getting 1 correct is 3/9,
    probability of getting 2 correct is P(1correct) * P(1 correct) = 9/81 =1/9
    probability of getting all 3 correct is P(1correct) * P(1 correct)* P(1correct) = 27/729 = 1/27

    I am not sure about how to approach the probability of getting none correct.
    1 minus P(1correct) ie 1-3/9 is a possibility but it may be more complicated than this. Any advice on how to approach this and comments on my tentative answers would be much appreciated.

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  2. #2
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    Quote Originally Posted by alexis2 View Post
    I wondered whether I was on the right track with regard to the following question:


    A student has to match three terms that she has never seen before with their definitions. If she guesses, what is the probability of her

    1. Getting all three correct?
    2. Getting none correct?
    3. Getting exactly one correct?
    4. Getting exactly two correct?

    What assumptions did you make? Do they seem reasonable?
    Hint: List the sample space.

    Using numbers to represent definitions and letters to represent terms, I think the sample space should be as follows:

    A1 B1 C1
    A2 B2 C2
    A3 B3 C3

    If we say that A3, B3 and C3 are correct, these are my tentative answers:

    probability of getting 1 correct is 3/9,
    probability of getting 2 correct is P(1correct) * P(1 correct) = 9/81 =1/9
    probability of getting all 3 correct is P(1correct) * P(1 correct)* P(1correct) = 27/729 = 1/27

    I am not sure about how to approach the probability of getting none correct.
    1 minus P(1correct) ie 1-3/9 is a possibility but it may be more complicated than this. Any advice on how to approach this and comments on my tentative answers would be much appreciated.
    Suppose the 3 words are A, B, C and the correct definitions are 1 for A, 2 for B and 3 for C.

    Here is the sample space..

    A1 B2 C3............all correct
    A1 B3 C2............one correct
    A2 B1 C3............one correct
    A2 B3 C1............none correct
    A3 B1 C2............none correct
    A3 B2 C1............one correct

    There are only 3!=6 possibilities.

    There is no chance of getting exactly 2 correct and 1 wrong,
    since if 2 are correctly matched, the 3rd will automatically be correctly matched.
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  3. #3
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    Quote Originally Posted by Archie Meade View Post
    Suppose the 3 words are A, B, C and the correct definitions are 1 for A, 2 for B and 3 for C.

    Here is the sample space..

    A1 B2 C3............all correct
    A1 B3 C2............one correct
    A2 B1 C3............one correct
    A2 B3 C1............none correct
    A3 B1 C2............none correct
    A3 B2 C1............one correct

    There are only 3!=6 possibilities.

    There is no chance of getting exactly 2 correct and 1 wrong,
    since if 2 are correctly matched, the 3rd will automatically be correctly matched.
    Thanks very much. I am still confused as to why there are only 6 possibilities...for example, why is the following combination not a possibility:

    A1 B2 C2 (this is not included above - why not?)

    It would be very helpful if you could clarify on this. Thanks again.
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  4. #4
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    Quote Originally Posted by alexis2 View Post
    Thanks very much. I am still confused as to why there are only 6 possibilities...for example, why is the following combination not a possibility:

    A1 B2 C2 (this is not included above - why not?)

    It would be very helpful if you could clarify on this. Thanks again.
    You see, if the student is given 3 terms and 3 definitions
    and is asked to match them up,
    she will not choose definition 2 to go with both word B and word C.

    She will place the 3 definitions with the 3 words,
    so that a different definition is given to each of the 3 words.

    One assumption would be.... she will choose a different definition for each word.
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  5. #5
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    Quote Originally Posted by Archie Meade View Post
    You see, if the student is given 3 terms and 3 definitions
    and is asked to match them up,
    she will not choose definition 2 to go with both word B and word C.

    She will place the 3 definitions with the 3 words,
    so that a different definition is given to each of the 3 words.

    One assumption would be.... she will choose a different definition for each word.
    Thanks - I think I get it...need to think about it more.
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  6. #6
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    Quote Originally Posted by alexis2 View Post
    Thanks - I think I get it...need to think about it more.
    She could place the same definition with 2 words, if she was happy to get 1 or 2 right.
    However she then has no chance of getting all 3 correct.
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  7. #7
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    Thanks.
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