You roll a standard six sided number cube. what is the probability of rolling a prime number or a greater number than 2?

5/6

Step-by-step explanation:

On a single number cube there are:

Prime numbers:  {1, 3, 5}

Number greater than 2:  {3, 4, 5, 6}

The desired probability is the sum of:  (a) the probability of getting a 1, 3 or 5     AND    (b) the probability of getting a number greater than 2.

These two probabilities are 3/6, or 1/2,  AND   4/6, or 2/3.

The union of these two events is the sum of 3/6 and 4/6:  7/6.  HOWEVER, this is not possible, because no probability can be greater than 1.

So:  Look at the possible outcomes {1, 3, 4, 5, 6}.  Only 2 is missing.   Thus, the probability of rolling a prime number or a number greater than 2 is 5/6.