I'm currently studying probabilities and I'm stuck on the following problem:
We collect cards of 3 different types, each time that we get a card, it is of the type "i" with the following probabilities : p1=1/2, p2=1/3, p3=1/6. Suppose that we just collected the 6th card, what's the probability that the collection is complete?
I have found 1 - ((1/2)^6 + (2/3)^6 + (5/6)^6 - (1/6)^6 - (1/3)^6 - (1/2)^6) = 125/216 but then it's asked to find an easier solution, the only hint available is "125/216 = (5/6)^3 ..." Any suggestions of what i could do with that?