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June 28th, 2017, 06:37 AM   #1
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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?
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June 28th, 2017, 08:20 AM   #2
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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.

$\displaystyle \begin{align}P(R \cup G \cup Y) &= P(R) + P(G) + P(Y) - P(R \cap G) - P(R \cap Y) - P(G \cap Y) + P(R \cup G \cup Y) \\&= 0.75^{12} + 0.75^{12} + 0.5^{12} - 0.5^{12} - 0.25^{12} - 0.25^{12} + 0 \\&\approx 0.06335\end{align}$
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June 28th, 2017, 10:07 AM   #3
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