# Thread: Probability - sampling with & without replacement

1. ## 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
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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?

2. Originally Posted by geton
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.
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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?
..