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Math Help - Probability - sampling with & without replacement

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    Probability - sampling with & without replacement

    Seven identical balls are marked respectively with the numbers 1 to 7 inclusive. The number on each ball represents the score for that ball. The seven balls are then put into a bag. If 2 balls are chosen at random one after the other, find the probability of obtaining a total score of 11 or more:
    (a) if the first ball is replaced
    (b) if the first ball is not replaced.


    If 2 balls are chosen at random one after the other from the 7 balls find, in case (a) and in case (b), the most probable total score for the 2 balls with its associated probability
    ---------------------------

    So far I thought,

    There are seven marked balls in a box.

    The probability to choose randomly first ball is 1/7. If first ball is replaced then the probability to choose randomly second ball is 1/7.

    2 balls have chosen randomly obtaining score 11 or more.
    These are (4, 7); (5, 6); (5, 7); (6, 7); (7, 4); (6, 5); (7, 5) and (7, 6)

    So now what to do?
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  2. #2
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    Quote Originally Posted by geton View Post
    Seven identical balls are marked respectively with the numbers 1 to 7 inclusive. The number on each ball represents the score for that ball. The seven balls are then put into a bag. If 2 balls are chosen at random one after the other, find the probability of obtaining a total score of 11 or more:
    (a) if the first ball is replaced

    Mr F says: This problem is the same as rolling a pair of seven sided dice and noting the sum of the spots on the two dice. So ..... start by drawing a grid.

    (b) if the first ball is not replaced.

    Mr F says: I suggest drawing a tree diagram.


    If 2 balls are chosen at random one after the other from the 7 balls find, in case (a) and in case (b), the most probable total score for the 2 balls with its associated probability

    Mr F says: Find the total score that has the greatest probability of occuring. A grid and a tree diagram will make it easier to see what the score is in each case.
    ---------------------------

    So far I thought,

    There are seven marked balls in a box.

    The probability to choose randomly first ball is 1/7. If first ball is replaced then the probability to choose randomly second ball is 1/7.

    2 balls have chosen randomly obtaining score 11 or more.
    These are (4, 7); (5, 6); (5, 7); (6, 7); (7, 4); (6, 5); (7, 5) and (7, 6)

    Mr F says: You should realise that the probability of each of these outcomes is 1/49.

    So now what to do?
    ..
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