the number on the cubes is 1,2,3,4,5,6
the probability of rolling a number less than 4 on each cube is equal to 3/6 which is equal to 1/2.
the probability or rolling a number less than 4 on both cubes is equal to 3/6 * 3/6 = 9/36 = 1/4
in general, if 2 events are completely independent of each other, then p(first event and second event) is equal to p(first event) * p(second event).
the rolling of one of the dice is completely independent of the rolling of the other dice, so the formula pplies.
in general also, if two or more events are mutually exclusive, then then p(first event or second event or third event) is equal to p(first event) + p(second event) + p(third event).
with any one of the dice, the probability of getting a 1 is 1/6 and a 2 is 1/6 and a 3 is 1/6.
since these events are mutually exclusive (on onel roll, you can't roll a 1 and a 2), then the formula applies.
that's how we get p(1 or 2 or 3) on one roll of the dice = 3/6.
that's how we get p(1 or 2 or 3) on the first roll and p(1 or 2 or 3) on the second roll) = 3/6 * 3/6 = 9/36 = 1/4.
