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June 28th, 2017, 06:37 AM  #1 
Newbie Joined: Jun 2017 From: Netherlands Posts: 2 Thanks: 0  Chance of a color missing
I have 12 spots and three colors. Each spot has a chance of being a certain color. 25% to be red 25% to be green 50% to be yellow. what is the chance a color will be missing?

June 28th, 2017, 08:20 AM  #2 
Senior Member Joined: Dec 2012 From: Hong Kong Posts: 853 Thanks: 311 Math Focus: Stochastic processes, statistical inference, data mining, computational linguistics 
Let R, G and Y denote the events that red, green and yellow are missing respectively. $\displaystyle \begin{align}P(R \cup G \cup Y) &= P(R) + P(G) + P(Y)  P(R \cap G)  P(R \cap Y)  P(G \cap Y) + P(R \cup G \cup Y) \\&= 0.75^{12} + 0.75^{12} + 0.5^{12}  0.5^{12}  0.25^{12}  0.25^{12} + 0 \\&\approx 0.06335\end{align}$ 
June 28th, 2017, 10:07 AM  #3 
Newbie Joined: Jun 2017 From: Netherlands Posts: 2 Thanks: 0 
thanks 

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chance, color, missing 
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