I have one red die and a green die. I want to find the probability of rolling at least one 4. Now, because they are 2 different dice, there are 36 possibilities.

  1. So the first possibility is a 4 from the red and some other number for the green.
  2. Second possibility is a 4 from the green and some other number for the red.
  3. Both roll a 4.

So I can clearly see that the answer is 3 ways. However, if I want to arrive at the answer using combinatoric equations, how would I do so?

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  • $\begingroup$ Errr...how can "3 ways" be an answer to finding a probability? $\endgroup$ – suomynonA Oct 6 '16 at 1:55
  • $\begingroup$ As @suomynonA pointed out, a probability is a number from 0 to 1 inclusive, so "3" is incorrect. $\endgroup$ – Joel Reyes Noche Oct 19 '16 at 1:29

Actually, there are more than three ways of rolling a four.

There are $1 \cdot6=6$ ways to roll a $4$ for the red and another number for the green, and $6\cdot1=6$ ways of rolling a $4$ for the green and another number for the red. Now, you subtract $1$ from the total, because you counted the combination $(6,6)$ twice. $12-1=11$, and there are $6\cdot6=36$ total possibilities, so the answer is $$\dfrac {11}{36}$$

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    $\begingroup$ Oh, I see my mistake now thank you! $\endgroup$ – Jonathan Oct 6 '16 at 2:11

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