Die Rolling Question about probability. So if I had a six sided die and rolled it six times what is the probability that I get a six, and why? I am only a sophomore in highschool so please don't talk about anything too advanced unless it is necessary to answer the question. Thanks!
 A: Rolling once the probability of rolling a 6 is 1/6 and the probability of not rolling a 6 is 5/6.  If you roll it twice the probability of rolling no sixes is 5/6 x 5/6 or, 25/36.  So, the probability of rolling at least one 6 is 1 - 25/36 or 11/36.
IF you roll it 6 times, the probability of getting at least one 6 is 1 - ((5/6) ^ 6) or about 66.5%.
If you are looking for the probability of rolling exactly one 6 that is equal to 1/6 x ((5/6) ^ 5) * 6, or about 40.2%.  The 1/6 is for rolling a 6; the (5/6)^5 is for not rolling a 6 5 times, the 6 is to account for the all the possible positions where the 6 comes up in the first through sixth rolls.
A: Let $A$ be the event "we got six in one of the rolls". Now remember that $P(A)=1-P(A^c)$. Lets calculate $P(A^c)$ because it is much simpler (where the $c$ stands for complement, i.e the event did no occur).
Now, if we want to calculate the probability that six was not the result of any of the experiments, the probability for that is:
$P(A^c)= (\frac {5}{6})^6$.
Now we use the complement formula and we get $$P(A)=1-P(A^c)=1- (\frac {5}{6})^6=0.665$$
