PROBABILITY: COMPLEMENTARY EVENTS

If the probability of an event, A, is P(A), then the probability that the event would not occur (also called the complementaery event) is 1 – P(A)

Example:

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What is the probability of not getting a white ball?

Solution:

Example:

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What is the probability of drawing a blue card?

Solution:

Let A = event of drawing a red card

B = event of drawing a blue card

P(B) is the probability of drawing a blue card which is also the same as the probability of not drawing a red card (Since the cards are either red or blue)

A and B are called complementary events. This may be denoted as:

P(A ’ ) = P(B) (recall in sets that A ’ is the complement of A)

P(A) = P(B ’ )

We can generally state that: P(A) + P(A ’ ) = 1

Example:

A number is chosen at random from a set of whole numbers from 1 to 50. Calculate the probability that the chosen number is not a perfect square.

Solution:

Let A be the event of choosing a perfect square.

Let A’ be the event that the number chosen is not a perfect square.

A = {1, 4, 9, 16, 25, 36, 49}

Number of elements in A, n(A) = 7

Total number of elements, n(S) = 50

The probability that the number chosen is not a perfect square is

The following video shows another example of calculating the probability of complementary events.

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