Question 994977
Probability is 0.12 that both happen.  You multiply.
Neither happens is 0.6*0.7=0.42.  You take the complement of each and multiply 
A or B happens.  0.4+0.3-P(both)=0.7-0.12=0.58
If they are mutually exclusive, then 
probability is 0 that both happen.  They can't by definition.
probability A or B happens is 0.7.  There is no double counting.
probability neither happens is 0.3.