Transcript Probability of Compound Events

Probability of Compound
Events
Review of Simple Probability
 The probability of a simple event is a ratio of the
number of favorable outcomes for the event to the
total number of possible outcomes of the event.
 The probability of an event a can be expressed as:
number of favorable outcomes
Pa  
total number of possible outcomes
Find Outcomes of simple events
 For Simple Events – count the outcomes
 Examples:
One Die- 6 outcomes
One coin- 2 outcomes
One deck of cards- 52 outcomes
One fair number cube- 6 outcomes
Finding Outcomes of more than one
event
 The total outcomes of each event are found
by using a tree diagram or by using the
fundamental counting principle.
 Example:
At football games, a student concession
stand sells sandwiches on either wheat or rye
bread. The sandwiches come with salami,
turkey, or ham, and either chips, a brownie,
or fruit. Use a tree diagram to determine the
number of possible sandwich combinations.
Tree diagram with sample space
Answer
 Using the fundamental counting principle
bread x meat x side
2 x
3 x 3 = 18 outcomes
Probability of Compound Events
 A compound event consists of two or more
simple events.
 Examples:
rolling a die and tossing a penny
spinning a spinner and drawing a card
tossing two dice
tossing two coins
Compound Events
 When the outcome of one event does not
affect the outcome of a second event, these
are called independent events.
 The probability of two independent events is
found by multiplying the probability of the
first event by the probability of the second
event.
Compound Event Notations
Independent Events
Example: Suppose you spin each of these two spinners. What
is the probability of spinning an even number and a vowel?
1
P(even) =
(3 evens out of 6 outcomes)
2
1
(1 vowel out of 5 outcomes)
P(vowel) =
5
1 1 1
 
P(even, vowel) =
2 5 10
1
6
P
S
5
2
O
T
3
4
R
Slide 10
Independent Events
Find the probability
 P(jack, factor of 12)
4
52
5
x
8
5
=
104
Slide 11
Independent Events
Find the probability
 P(6, not 5)
1
6
5
x
6
5
=
36
Slide 12
Probability of Compound events
P(jack, tails)
4 1
4
( )
 0.04  4%
52 2
104
Dependent Event
 What happens during the second event
depends upon what happened before.
 In other words, the result of the second event will
change because of what happened first.
The probability of two dependent events, A and B, is equal to the
probability of event A times the probability of event B. However,
the probability of event B now depends on event A.
P(A, B) = P(A)  P(B)
Slide 14
Dependent Event
Example: There are 6 black pens and 8 blue pens in a jar. If you
take a pen without looking and then take another pen without
replacing the first, what is the probability that you will get 2
black pens?
P(black first) =
6
3
or
14
7
5
P(black second) =
(There are 13 pens left and 5 are black)
13
THEREFORE………………………………………………
P(black, black) =
3 5
15

or
7 13
91
Slide 15
Practice
1. P(heads, hearts) =
2. P(tails, face card) =
Your turn
 Create your own independent compound
event problem. Then, exchange with your
seat partner.