Explain what is meant by complementary events and how it could be calculated.

The complementary of an event is that the event does not happen. 

For example the event to you role a six faced die and get a 3 has a complementary event that you will get either a 1, 2,4,5, or 6. 
complementary event and the event can not happen in the same time.

P( event)+P(complementary event) =1

P( complementary event)= 1-P(event)

If we have to calculate the probability of getting either a 1, 2, 4, 5, or 6 on your next role of a die we can make our life easy and say we have to calculate the probability of getting not getting a 3. 

P( 3) = 1/6
P (not getting 3) =1-1/6=5/6