You roll a standard number cube. find p(number is not 3). a. 1/6 b. 2/3 c. 5/6 d. 1/2

There are 6 possible outcomes {1,2,3,4,5,6} which makes up the sample space.

The event space is the set of items in which we want to happen, which is this set {1,2,4,5,6}. Basically this is the set mentioned earlier but we kicked out '3'.

There are 5 items in the event space out of 6 items in the sample space. This is why the answer is C) 5/6


Or you can think of it this way:

The probability of rolling a "3" is 1/6 because there is one "3" out of 6 total

The probability of not rolling a 3 is going to be 1 minus that result
P(not rolling 3) = 1 - P(rolling a 3)
P(not rolling 3) = 1 - (1/6)
P(not rolling 3) = 6/6 - 1/6
P(not rolling 3) = (6-1)/6
P(not rolling 3) = 5/6

Either way, the answer is 5/6