Confusion understanding probability I am a beginner in this forum - please don't judge me too harsh.
I understand that my question is noobie but I read a lot and couldn't understand the concept of summing probabilities.
Here is the problem I cannot understand:
We have a dice with 6 possible outcomes 1...6.
Rolling the dice once, the chance to hit 3 is 1/6
What is the chance to hit 3 if I throw the dice 6 times or 8 times?
Simply summing the probabilities doesn't make sense to me.
I mean 1/6 + 1/6 + 1/6 + 1/6 + 1/6 + 1/6 + 1/6 + 1/6  = 8/6 is greater than 1. How come probability gets greater than 1?
My reasoning must be wrong

If you want to have the probability of hitting ONLY once 3, a favoruable event is this
$$\{3,\overline{3},\overline{3},\overline{3},\overline{3},\overline{3}\}$$
where with $\overline{3}$ I mean "not 3"
This probability is $\frac{1}{6}\times\left(\frac{5}{6}\right)^5$ because all this events must happen together.
Now you can understand that the "3" can be hit in any of the six positions, thus this probability must be multiplied by 6
Concluding, the probability to hit exactly one 3 in 6 dice's rolls is
$$6\times\frac{1}{6}\times\left(\frac{5}{6}\right)^5$$
