Complementary Events

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
-