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There are 200 balls in a bag, seven different colors: Red, Blue, Black, Yellow, Green, White and Pink.

Is there a way to know the probability of chosing 22 red balls and 23 blue balls if I don't know how many balls of each color there are in the bag?

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  • $\begingroup$ My inclination is that it's possible in theory, since there's only a finite number of possibilities for how the 200 balls are distributed between colors. I don't know how you'd go about actually computing it, though. $\endgroup$
    – DylanSp
    Jan 28 '16 at 22:06
  • $\begingroup$ @DylanSp But there you're calculating the probability of a particular configuration of the bag; a probability of a probability (if you like). I don't think that's what OP is after. $\endgroup$ Jan 28 '16 at 22:10
  • $\begingroup$ Actually, wait - I assumed that we'd be choosing 45 balls from the bag and you wanted to know the probability that those 45 balls were exactly 22 red balls and 23 green. Do you mean the probability that the bag has exactly 22 reds and exactly 23 greens? $\endgroup$
    – DylanSp
    Jan 28 '16 at 22:11
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No, not unless you assume equiprobability (there is an equal amount of each) where in this case it's impossible, since 200 is not a multiple of 7.

There just isn't enough information.

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