Complementary events are two outcomes of an event that are the only two possible outcomes.
Mutually exclusive events are two or more outcomes of an event that cannot occur at the same time.
All complementary events are mutually exclusive, but all mutually exclusive events are not necessarily complementary.
Let's note each Example as complementary, mutually exclusive, both, or neither.
Note: the piggy bank contains a Quarter (25 cents), Dime (10 cents), Nickel (5 cents), and Penny (1 cent)
Picking one coin from the piggy bank and getting a dime or a nickel.
Mutually exclusive? Yes. You can't pick a dime and a nickel at the same time
Complementary? No. There are other options, like a penny or quarter
Picking a coin from the piggy bank and getting a quarter or a coin divisible by 5.
Mutually exclusive? No
Quarters are also divisible by 5 (as well as dimes and nickels), so these are not mutually exclusive nor are they complementary.
Choosing one marble from the bag and getting a blue or a green one.
Mutually exclusive? Yes. You can't choose a marble that is both blue and green at the same time.
Complementary? No. There are other options (like an orange one).
Rolling a die and getting an odd number or a 4.
Rolling a die and getting an even number or a four.
Rolling a die and getting an odd number or an even number.