SOLUTION: In an urn there are 3 white and 4 black marbles. They are taken out of the urn one by one. What is the chance of the first and last marble being white?

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Question 1195011: In an urn there are 3 white and 4 black marbles. They are taken out of the urn one by one. What is the chance of the first and last marble being white?
Found 2 solutions by ikleyn, greenestamps:
Answer by ikleyn(52776) About Me  (Show Source):
You can put this solution on YOUR website!
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In an urn there are 3 white and 4 black marbles. They are taken out of the urn one by one.
What is the chance of the first and last marble being white?
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In all, there are 3+4 = 7 marbles.


There are  7%21%2F%283%21%2A4%21%29 = 35 possible DISTINGUISHABLE permutations of these marbles. 
It is the number of all possible distinguishable outcomes of the experiment.


Of these 35 distinguishable permutations, there are 5 distinguishable permutations, 
where white marbles are in the 1-st and in the last, 7-th position, and in some 
position between 2-nd and 6-th for the remaining third white marble.


Therefore, the sough probability is  P = 5%2F35 = 1%2F7.    ANSWER

Solved.



Answer by greenestamps(13198) About Me  (Show Source):
You can put this solution on YOUR website!


The total number of ways of arranging 3 white marbles and 4 black marbles is

%283%2B4%29%21%2F%28%283%21%29%284%21%29%29+=+35

With white marbles in the first and last positions, the number of ways of arranging the remaining 1 white marble and 4 black marbles is

%281%2B4%29%21%2F%28%281%21%29%284%21%29%29+=+5

So the probability that the first and last marbles are both white is 5/35=1/7.