If a standard 6-sided die is rolled, what is the probability that the result will be at least 3 or an even number?

The outcomes that satisfy the given requirement are
#color(white)("XXX"){4,5,6} uu {2}#

The cardinality (number of elements) in this collection is #4#.

The cardinality of all possible outcomes, of the set #{1,2,3,4,5,6}#, is #6#

The probability of satisfying the given requirement is
#color(white)("XXX")4" out of "6#
#color(white)("XXX")#or
#color(white)("XXX")4/6 = 2/3#

Two conditions are specified, but we need to note the use of the word "OR". This widens the options, because we want to have

Either a number greater than 3 (which can be #4,5,6#)
OR an even number (which can be #2,4,6#)

"OR" in probability implies that we have to ADD the probabilities.

However in this case the outcomes are not mutually exclusive; it is possible to have a number that is greater than 3 as well being an even number. These may not be counted twice.

Let G be 'Greater than 3' and E be 'Even'.

#P(G " or " E) = P(G)+ P(E) -P(G and E)#

#P(G " or "E) = 3/6 +3/6 - 2/6 = 4/6#

#= 2/3#

We could also just list the possible outcomes and count the ones that meet the conditions:

#1," "color(red)(2)," "3," "color(red)(4)," "color(red)(5)," "color(red)(6)#

#P(G" or "E) = 4/6 = 2/3#