Viceroy63 wrote:Ok; I follow this thread so far but can any one calculate the odds of getting a rainbow (one card of each color) in 4 cards? Now that I would like to see done.
Boys, break out your calculators?
Oh; And how come we don't have joker spoils? Does anyone know?
I think that is a good question.
Given that you don't already have a rainbow? Then it's easy cuz you either have 2 of 1 color and 1 of another color or all 3 of the same color. If it's the latter, which only occurs 1/9 of the time, you know you won't be getting a rainbow. But in the 8/9 times that's not the case, you need 1 of the missing color giving you a 1/3 chance of getting a 4-card rainbow, given that you don't have a rainbow in 3 cards. So, you'd have an 8/27 or 30%
If you are starting from scratch and just want to know the odds of getting a rainbow given any four cards, then odds are slightly more complicated.
Your first card is X-colored. The other two colors are now Y and Z.
You need at least 1 Y and at least 1 Z in the next 3 cards.
1/3 chance of getting another X, in which case you need a Y and a Z to come out: odds 2/3*1/3 = 2/9
2/3 chance of getting a Y (i.e. anything but X), in which case you need a Z to come out. The chances of not getting a Z in these next two cards is 2/3*2/3 = 4/9. That means you have a 5/9 chance of getting a Z.
So, 1/3*2/9 + 2/3*5/9 = 2/27 +10/27 = 12/27.
You have a 12/27 or 44% chance of getting a rainbow in 4 cards.