Identify complementary events and use the sum of probabilities to solve problems (VCMSP294)

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

Know:

  • That the probability of all chance experiments ranges from 0 to 1.

  • How to add decimal numbers.

  • Events can be complementary or not complementary.

Understand:

  • That the probability of all complementary events always equals 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 can be 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 use the information to figure out the probabilities of the events.

For example, if the sum of complementary events always have to add up to 1 or 100% 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 a specific event occurring using the sum of probabilities for 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 calculating the sum of the chances 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 or 1.

eg.) probability of rolling a 6 is 1 out of 6, 1/6. The probability of rolling a number 5 or less would be 1 – 1/6 = 5/6 or 5 out of 6 chance.

Complementary Events Videos