Complementary events are two events where the probability of one happening plus the probability of the other not happening equals 1. For example, with a standard six-sided die, the probability of rolling greater than 4 is 1/3, and the probability of rolling less than or equal to 4 (the complement) is 2/3, which sums to 1. The probability of an event can also be found by subtracting the probability of its complement from 1. For example, in drawing a ball from an urn with 5 white, 3 black, and 2 red balls, the probability of not drawing a red ball is 10/10, which is 1 minus the probability of drawing a red ball, 2/10.

1. 1
Complementary
Probability

2. 2
E = {winning a race}
Complement of E = {loosing a race}Complement of E = {NOT winning a race}
Example:
Complementary Events

3. 3
Complementary Events –
the events of one
outcome happening and
that outcomes not
happening are
complimentary; the sum
of the probabilities of
complementary events is
1.

4. 4
Example: Deck of Cards.
What is the probability of picking a heart?
# favorable outcomes 13 1
# possible outcomes 52 4
The probability of picking a heart is
1 out of 4 or .25 or 25%
What is the probability of picking a not heart?
# favorable outcomes 39 3
# possible outcomes 52 4
The probability of picking a heart is
3 out of 4 or .75 or 75%
Probability of Simple Events
P(heart) = = =
P(not heart) = = =

5. 5

6. 6
The Sum of the Probabilities of an
Event and its Complement add to ‘1’.
Example: For a dice
P(>4) =
2
6
=
1
3
P(Complement >4) = P(≤4) =
4
6
=
2
3
P(>4) + P(Complement >4) = 1
3
+
2
3
= 1
Complementary Events

7. 7
Finding the Probability of an Event to
happen, is by Subtracting the
Probability that it won’t happen from
One (1) .

8. 8
EXAMPLE 1: An Urn contains 5 white, 3
black, 2 red balls. In getting one ball, what
is the probability that it is not a red ball?

9. 9
Real World Example 2:
A computer company
manufactures 2,500 computers
each day. An average of
2,400 of these computers are
sold with no defects. What is
the probability that the
computer you purchased is
defective?

10. 10
P(Defective) =
= 1
2,400
2,500
- P(Not Defective)1
-