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

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*A*) + P(*A* ’ ) = 1

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The Probability of Complementary Events

1. A standard deck of cards has 52 cards.

a) What is the probability of drawing an ace from the shuffled deck of cards?

b) What is the probability of drawing anything but an ace?

2. A bag contains 12 identically shaped blocks, 3 of which are red and the remainder are green. The bag is well shaken and a single block is drawn.

a) What is the probability that the block is red?

b) What is the probability that the block is not red?

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

You can use the free Mathway calculator and problem solver below to practice Algebra or other math topics. Try the given examples, or type in your own problem and check your answer with the step-by-step explanations.

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More lessons on Probability

**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* ’ )

*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

1. A standard deck of cards has 52 cards.

a) What is the probability of drawing an ace from the shuffled deck of cards?

b) What is the probability of drawing anything but an ace?

2. A bag contains 12 identically shaped blocks, 3 of which are red and the remainder are green. The bag is well shaken and a single block is drawn.

a) What is the probability that the block is red?

b) What is the probability that the block is not red?

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You can use the free Mathway calculator and problem solver below to practice Algebra or other math topics. Try the given examples, or type in your own problem and check your answer with the step-by-step explanations.

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