1 Press Ctrl-A ©G Dear 2010 – Not to be sold/Free to use ComplementaryEvents Stage 6 - Year 11 Applied Mathematic (Preliminary General 1)

2 Definition The Complementary Event is the event that describes all other possible events. Ewinning E = {winning a race} Complement of Eloosing Complement of E = {loosing a race} Complement of ENOTwinning Complement of E = {NOT winning a race} Example: Complementary Events (1/3)

3 EventComplement1 The Sum of the Probabilities of an Event and its Complement add to ‘1’. Example: Example: For a dice P(>4) = 2626 = 1313 P( Complement >4) = P(≤4) = 4646 = 2323 P(>4) + P( Complement >4) = = 1 Complementary Events (2/3)

4 Event subtract Complement1 To find the Probability of an Event, subtract the probability of its Complement from ‘1’. Example: Example: For a standard pack of cards P(Spot Card) = = P( Not Spot Card) 1 - = Complementary Events (3/3)