I'm selecting 164 items from a bag of 394. What is the probability that exactly 162 of these items will be green if there are 264 green items in the bag?
I calculated this by multiplying the probability of selecting a green object on the first try (264/394) by the probability of selecting a green object on the second try (263/393) by the probability of selecting a green object on the third try (262/392) and so on and so forth 162 times. Then I multiply this product by the probability that the last two draw are NOT green (130/232)*(129/231).
This results in a crazy small number. I just don't think this makes sense because if I follow this logic and calculate the probability of selecting 110 green objects and 54 non-green objects, which would result in a sample that matches the distribution of the population, I also get a very small probability.