1

ComplementaryProbability

2

E = {winning a race}

Complement of E = {loosing a race}

Complement of E = {NOT winning a race}

Example:

Complementary Events

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

Example: Deck of Cards.What is the probability of picking a

heart? # favorable outcomes 13 1 # possible outcomes 52 4The probability of picking a heart is1 out of 4 or .25 or 25%

What is the probability of picking a not heart?

# favorable outcomes 39 3 # possible outcomes 52 4The probability of picking a heart is3 out of 4 or .75 or 75%

Probability of Simple Events

P(heart) = = =

P(not heart) = = =

5

 

6

The Sum of the Probabilities of an Event and its Complement add to

‘1’.Example: For a diceP(>4) =2

6 = 13

P( Complement >4) =P(≤4) =46 = 2

3

P(>4) +P( Complement >4) =13 + 23 = 1

Complementary Events

7

Finding the Probability of an Event to happen, is by Subtracting the

Probability that it won’t happen from One (1) .

 

 

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

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

P(Defective) =

= 1 2,4002,500

- P( Not Defective)1

-