Event Not Occuring

Question

What is the probability that you will not roll doubles when rolling two fair three sided dice (the sides are numbered 1-3 on each die)?

Answer 1

The probability that an event will not occur is equal to 1 minus the probability that it will occur.  

 

The probability that you will roll doubles is 1/3 (if you have trouble seeing why, imagine rolling the second die after the first.  You will only get doubles if the second roll is the same as the first, which has probability 1/3).  

 

So the probability that you will not roll doubles is 1 - (1/3) = 2/3