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Math Help - I really need help for this probability question :(

  1. #1
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    I really need help for this probability question :(

    The letters A, B, C, D, E, F, G are arranged around a circle. Find the probability that A and B are not together.

    It's a probability homework question, and i'm really struggling to get my head around this kind of probability
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  2. #2
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    ignore the circle and consider the 3 points around A.

    i will use "x" to denote an unknown letter.

    The total number of arrangements of xAx = 6 * 1 * 5 = 30

    You want to exclude the cases where B is on the left of A
    BAx = 1 * 1 * 5 = 5

    And the cases where B is on the right of A
    xAB = 5 * 1 * 1 = 5

    So, there are 10 arrangements where A and B are together.

    Probability = 1 - 10/30 = 2/3





    Warning my answers on these types of questions tend to be very unreliable
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  3. #3
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    Quote Originally Posted by phillychum View Post
    The letters A, B, C, D, E, F, G are arranged around a circle. Find the probability that A and B are not together.

    It's a probability homework question, and i'm really struggling to get my head around this kind of probability
    Another approach is to count the number of ways that A and B are together by considering the arrangements of AB, C, D, E, F, G (5!) and BA, C, D, E, F, G (5!). Divide this by the number of arrangements of A, B, C, D, E, F, G (6!) and subtract the result from 1.
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  4. #4
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    Quote Originally Posted by phillychum View Post
    The letters A, B, C, D, E, F, G are arranged around a circle. Find the probability that A and B are not together.

    It's a probability homework question, and i'm really struggling to get my head around this kind of probability
    "A" can be in any of 7 positions around the table.

    Whichever position it is in, B has a \frac{4}{6} chance of not being next to "A", as there are 4 of the remaining 6 positions not adjacent to "A".

    The probability of "A" not being next to "B" is \frac{2}{3} wherever "A" happens to be.
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