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“. 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, you can be an even number or not an even number, but nothing else!   

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)

Complementary Events Videos

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