probability of an event happening over a year If I am calculating the probability of something happening over a year and there is say a 10 percent chance per month it will happen I know that if it happened say in August, September and October I would do, .10*.10*.10 which is 1/1000,
but how would I calculate the probability of it happening once from June to August?
 A: There are three options: either it happened in June (and didn't happen in July and August), in July alone or in August alone.
The probability that it happened in one of the months, say June, and not happened in the others, is, similar to what you said: $0.10 \cdot 0.90 \cdot 0.90$ (there is a $90$% chance it won't happen). Therefore the solution is $3 \cdot 0.10 \cdot 0.90 \cdot 0.90$.
A: Probabilities are actually easy to calculate with, as long as the individual events are independent of each other:
If you are looking for an and (i.e. A and B happens), you multiply the probabilities. If the probability for A is 50% and for B 10%, the probability that both A and B happen is 0.5*0.1 = 0.05 = 5%.
If you are looking for an or (i.e. either A or B or both happen), you sum the inverse of the probability and substract it from 1. With the above A and B, the probability that either (or both) happen is 1 - (1-0.5) * (1-0.1) = 1 - 0.5 * 0.9 = 1 - 0.45 = 0.55 or 55%
This follows from fundamental logic and De Morgan's Law:

*

*A + !A = 1

*!(A or B) = !A and !B

