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# s1 probability q watch

1. seven identical balls are marlked respectively with the numbers 1 to 7, representing the score for that ball. they are put into a bag and 2 balls are chosen at random one after the other
find the proability of obtaining a total score of 11 or more if
a) the first ball is replaced 10/49 got that
b) the first ball is not replaced
(i dont know that one)

and if 2 balls are chosen at random from the seven balls find in case A) and B) the probable total scores for the two balls with its associated probability

2. (Original post by ruth_lou)
seven identical balls are marlked respectively with the numbers 1 to 7, representing the score for that ball. they are put into a bag and 2 balls are chosen at random one after the other
find the proability of obtaining a total score of 11 or more if
a) the first ball is replaced 10/49 got that
b) the first ball is not replaced
(i dont know that one)

and if 2 balls are chosen at random from the seven balls find in case A) and B) the probable total scores for the two balls with its associated probability

The different ways of getting 11 are :-
4,7 or 5,6 or 6,5 or 7,4

Chance of getting either a 4,5,6 or 7 is 4/11. Then if you keep hold of that ball, there are 10 left and you *need* to get a certain one (to make your total 11) So the probability of getting the one you need is 1/10
So you do 4/11 x 1/10 = 4/110 = 2/55

Next part :-
You could make a quick list of the different ways you get each total:-
eg:-
Total of 2 = 1 way (1,1)
Total of 3 = 2 ways (1,2) (2,1)
Total of 4 = 3 ways (1,3) (2,2) (1,3)
Total of 5 = 4 ways etc
Total of 6 = 5 ways
Total of 7 = 5 ways
Total of 8 = 7 ways
Total of 9 = 6 ways
Total of 10 = 5 ways
Total of 11 = 4 ways
Total of 12 = 3 ways
Total of 13 = 2 ways
Total of 14 = 1 ways
So the you are most likely to get a total of 8

Then if you're not replacing ur first ball :-
If you get a ONE on your first ball, then you could get a total of (3,4,5,6,7,8)
If you get a TWO on your first ball, then you could get a total of (3,5,6,7,8,9)
If you get a THREE on your first ball, then you could get a total of (4,5,7,8,9,10)
If you get a FOUR on your first ball, then you could get a total of (5,6,7,9,10,11)
If you get a FIVE on your first ball, then you could get a total of (6,7,8,9,11,12)
If you get a SIX on your first ball, then you could get a total of (7,8,9,10,11,13)
If you get a SEVEN on your first ball, then you could get a total of (8,9,10,11,12,13)
Then count how many each number occurs and that will give you the probabilities.

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Updated: June 8, 2005
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