How can I add two probabilities with the same time?
Emily Wong 
When I have two probabilities at the same time or at different time how can I add them together? I know that simply add them doesn't work because that is just for two probabilities independent or mutual exclusive. Do I need to normalize the two probabilities? Why can't I simply add them together? Is there a reason? With two probabilities I mean I've two dice with 6 side. When the probability of dice 1 and side 1 is 1:6 and it's the same for dice 2 how can I combine them together? There is this rule about mutual exclusive or independent but I also have read about the other rule of the same time. Is there a probabilities that both dice have the same side at the same time?
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$\begingroup$If you want to combine the probabilities, you have to decide what event you want. If you want the chance that both dice come up $1$, the events are independent and you multiply them: $\frac 16 \cdot \frac 16=\frac 1{36}$. If you want the chance that either one comes up and they were exclusive, you would add them. In this case they are not exclusive-both dice can come up $1$. The chance that at least one of them comes up $1$ is $\frac 16 + \frac 16 - \frac 1{36}=\frac {11}{36}$ The subtraction of $\frac 1 {36}$ is because we have double counted the case where they both came up $1$-it is part of both $\frac 16$'s.
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