Complementary Events and Sum of Probabilities. (8)

Identify complementary events and use the sum of probabilities to solve problems (ACMSP204)

LO: To identify complementary events and use the sum of probabilities to solve problems.

Know:

  • That all the probability of a chance experiment ranges from 0 to 1.
  • How to add decimal numbers.
  • how to calculate elapsed time
  • Events can be complementary or not complementary.

Understand:

  • That all complementary events equal to 1.

Do:

  • I can identify complementary events and use the sum of probabilities to solve problems..

Complementary Events

Complementary events are “opposite events“. In probability, the event of success (the event happens) or failure (the event not happening) can be classified as a complementary event. For example, the chances of rolling a 5 and the chances of not rolling a 5 are complementary events.

The probability of complementary events always add up to 1 (for 100%), because there are no other options.

For example, you can be blue or not blue (blue’), you can be an even number or not an even number, but nothing else! 

A very common misunderstanding is that events have to be equally likely. In reality, this does not necessarily need to be the case.  

Sum of Probabilities

With complementary events, you can always figure out the probabilities.

For example, if the sum of complementary events always have to add up to 1 and the probability of flipping a heads is 52% P(heads) = 0.52, then the probability of flipping a tails must be 48% which is P(tails) = 0.48.

P(coin toss) = 1
P(coin toss) = P(heads) + P(tails)
1 = 0.52 + P(tails)
1 – 0.52 = P(tails)
P(tails) = 0.48)

We can then easily calculate the probability of an event occurring using complementary events. For example, what is the chance that I will roll a number 5 or less? We can do it the long way of adding each chance of landing 1, 2, 3, 4 and 5. Or we can do it quicker by finding the chance of landing a 6, then subtracting that from 100.

Complementary Events Videos