Explanation:
2/3 of the doughnuts in a box have frosting.
1/2 of the doughnuts with frosting have sprinkles.
to combine this into one event with both conditions true (doughnuts with frosting and sprinkles) we need to multiply the fractions :
2/3 × 1/2 = (2×1)/(3×2) = 2/6 = 1/3
it is only logical : half of 2/3 is 1/3.
so, 1/3 of the doughnuts in the box have both frosting and sprinkles.
FYI : if the question was "how many have either frosting or sprinkles", we would have to add the non-overlapping parts (instead of multiplying). it is important to remember the key word "non-overlapping" in this regard.
in our case both conditions are fully overlapping (as only frosted doughnuts have sprinkles). and so the answer would be 2/3 + 0 = 2/3.
if the situation were to be e.g. that 2/3 are frosted, and half of the others have sprinkles, then the 2 conditions would not overlap, and the answer would be
2/3 + 1/3 × 1/2 = 2/3 + 1/6 = 4/6 + 1/6 = 5/6