Download 23. GENERATING SAMPLE SPACE (tree diagram)

Probability and Simulation
GENERATING SAMPLE SPACE
Listing All Possible Outcomes of
a Probabilistic Experiment
•
Enumeration
•
Tree diagrams
•
Additional methods – counting
fundamentals
EXAMPLE
Three Children Example
•
•
•
A couple wants to have exactly 3
children. Assume that each child
is either a boy or a girl and that
each is a single birth.
List all possible orderings for the
3 children.
Enumeration
1st Child 2nd Child 3rd Child
B
B
B
G
B
B
B
G
B
B
G
G
B
B
G
B
G
G
B
G
G
G
G
G
S={BBB, GBB, BGB, BBG, GGB, GBG, BGG, GGG}
Tree Diagrams
1st Child __
2nd Child
B
B
G
B
G
G
__
3rd Child
B
G
B
G
B
G
B
G
BBB
BBG
BGB
BGG
GBB
GBG
GGB
GGG
S={BBB, BBG, BGB, BGG, GBB, GBG, GGB, GGG}
PRACTICE:Using the previous
conditions, what is the probability of
these events from happening?
P(of getting 2 consecutive boys)
=2.5
P(of getting a boy then a girl)
=.25
P(of getting all boys)
P(of having a girl as a third
child)
P(of having 2 girls)
=.125
=.50
=.375
A glass jar contains 6 red, 5 green, 8 blue and 3
yellow marbles. If a single marble is chosen at
random from the jar, what is the probability of
choosing a red marble? a green marble? a blue
marble? a yellow marble?
P[red]
=
.27P[green]
.23P[blue]
.36P[yellow]
=
=
= .14
NOTE!
Being able to properly enumerate the
outcomes in a sample space will be
critical in determining probabilities.
Enumeration and tree diagram will be
very helpful to eliminate in accidentally
overlooking any outcomes
Organize a list of possible
outcomes when you toss a
coin 4 times
0 heads
1 head
2 heads
3 heads
4 heads
TTTT
HTTT
HHTT
HHHT
HHHH
THTT
HTHT
HHTH
TTHT
HTTH
HTHH
TTTH
THHT
THHH
THTH
TTHH
Multiplication Principle:
If you can do one task in x1 number of
ways and a second task in x2 number of
ways, then both can be done in (x1) (x2)
number of ways
Example:
Sample space of tossing a coin 3
times: 2 x 2 x 2 = 8
WHICH ONE ARE YOU?
Odds For Meeting A FemaleThe probability
of a young man meeting a desirable and
receptive young female increases by
exponential progression when he is already
in the company of:
(1) a date
(2) his wife
(3) a better looking and richer male friend