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In everyday life we use the word complementary to describe things that go together to make a complete picture. For example, a hat and a dress are complementary parts of a complete outfit.
Do not confuse 'complementary' with 'complimentary'. The 'i' word refers to talking nicely to someone, and paying them a 'compliment'.
In probability, complementary events make up all the possible outcomes. For coin tossing, getting heads and getting tails are complementary events. When you toss a coin you either get a Head or a Tail.
Other examples of complementary events that you might investigate in probability events include:
| Event | Complementary number | | Rolling a 6 with a single throw of a die | Rolling any number from 1 to 5 | | Rolling an even number | Rolling an odd number | | Rolling a factor of 6 (1,2,3 or 6) | Rolling a 4 or 5 | Tossing two coins:
Same results (TT or HH) | Different results | | Tossing two coins: No Heads | Two Tails | | Tossing three coins: getting 3 heads | Getting one or more Tails | | Tossing three coins: results (HHH or TTT) | Different results |
Therefore the probability of getting the event plus the probability of getting the complementary events must add to equal 1 - the total probability for the situation.
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