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statistics - picking marbles, confused! Watch

1. There are 16 different coloured marbles in bag 1.

12 of the 16 marbles are then picked at random and put in a separate bag (bag 2).

I then pick 4 marbles at random out of these 12 (bag 2).

I like 4 of the 16 original differently coloured marbles. What are the odds that I like the colour of the 4 marbles that I have just picked from the 12 (bag 2)?
2. (Original post by X123)
There are 16 different coloured marbles in bag 1.

12 of the 16 marbles are then picked at random and put in a separate bag (bag 2).

I then pick 4 marbles at random out of these 12 (bag 2).

I like 4 of the 16 original differently coloured marbles. What are the odds that I like the colour of the 4 marbles that I have just picked from the 12 (bag 2)?
There are two ways you can look at this using combinations that I can see:

Either, it seems obvious that you are asked to choose a specific 4 from 16, since the intermediate choice is random.

Or, consider probability of choosing 12 from 16 such that your 4 desired marbles are present, times the probability of choosing the specific 4 from 12.

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Updated: December 30, 2010
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