AND = MULTIPLY the probabilities.
OR = ADD the probabilities.
Intuitively, if you multiply two fractions the result will be a smaller number, showing the lower likelihood of both events occurring at the same time--AND. However, adding two fractions creates a larger number, meaning there is a greater chance of either event occurring--OR.
Ex: If probability of x = 1/4, y = 1/2, & z = 5/8, & you are looking for the probability of x & y, but not z EQUALS: (1/4)(1/2)(1-(5/8)) = (1/8)(3/8) = 3/64