The probability of an event occurring given a discrete number of possibilities is given by #"number of ways the event can occur"/"number of total possibilities"#
Given the roll of a single die, there are #6# total possibilities (a roll of #1, 2, 3, 4, 5#, or #6#).
#a)# As there are #3# possible even numbers which can be obtained by rolling a die (#2, 4#, or #6#), the probability of rolling an even number is #3/6 = 1/2#
#b)# As there are #4# possible numbers greater than #2# (#3, 4, 5#, or #6#), the probability is #4/6 = 2/3#
#c)# As there are #3# possible odd numbers (#1, 3#, or #5#), the probability is #3/6 = 1/2#
#d)# As there are #2# possible numbers which are divisible by #3# (#3# or #6#), the probability is #2/6 = 1/3#
