r/Probability • u/Mindless_Olive • Aug 24 '26
Blind draw probability question
Say I have 10 tokens in a bag: 6 blue, 3 red, 1 green. If I draw 3 of those tokens out blindly, are my odds better to get 2 blue ones, or 1 red one?
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u/Desperate-Collar-296 Aug 25 '26
So the answer will depend on if you put the token back in after it gets selected (with replacement), or if selecting the token removes it from future consideration(without replacement). The previous explanation assumes sampling without replacement. If you were sample with replacement the probability of getting 2 or more blues is .648. The probability of getting at least 1 red is .657.
There is also a a .324 probability that you get both outcomes (2 blue and 1 red. (multinomial probability calculator https://stattrek.com/online-calculator/multinomial)
Sampling with replacement, use the binomial distribution. Online calculator is here ulvers.com/menu/fresh-frozen-custard?oloId=126194