1. The problem statement, all variables and given/known data An ordinary die is painted red on two sides, white on two sides and blue on two sides. Find the probability we get no reds in 12 rolls of the die. 2. Relevant equations 3. The attempt at a solution GENERAL QUESTION: I thought this would be a binomial distribution, but the book says it's geometric. I seem to have an issue between binomial, geometric, and negative binomial. I realize in binomial your random variable is the number of successes across a fixed # of independent trials, the negative binomial is the number of trials to get a fixed number of successes, and that a geometric is the number of trials to obtain the first success (which is a special case of the negative binomial). If there could be any way to clear this up, that'd be great. I've watched videos, etc. and I'm still struggling with determining the distributions. ATTEMPT: There is a fixed number of trials (n =12), the outcomes are dichotomized (Success = No Red, Fail = Red), there is a constant probability among all trials (p = 2/3), and each trial is independent. Letting X = number of red colors face up. This leads me to believe x ~ binomial (n=12, p=2/3). (I don't need to plug into the formula, as that's not where I'm confused). Meaning P(x=0). The book says it is X = # of rolls to get a red side. x ~ Geometric(p =p("fail") = 1/3). And then would p(x=1)? Is there any distinct way to separate which distribution to use, especially between these 3? I kind of see why they say its geometric, but I also don't see why mine is wrong.