Transcript The Counting Principle

Probability & Statistics
The Counting Principle
Section 12-1
Independent Events

Independent events
 When the occurrence of one event does not
affect the occurrence of another event.
Example 1
event 1: a sunny day
event 2: a Tuesday
A sunny day will have no bearing on whether it is a Tuesday.
The fact that a day is a Tuesday will not impact whether it
will be sunny.
Example 2
From a deck of 52 playing cards a person randomly selects 1
card, replaces it, and selects another card.
Important Definitions
 Dependent

events
When the occurrence of one event
affects the occurrence of another event.
Example 1
event 1: A snowy winter
event 2: people skiing
If we have a snowy winter, that will affect the number
of people who go skiing.
Example 2
From a deck of 52 playing cards a person randomly selects 1
card, without replacing it, and selects another card.
Using the Counting Principle
You are in the yearbook club and it has 5
officers: 3 boys and 2 girls.
 You all want to propose a big change to
the yearbook so you want two officers to
speak to Ms. Langan.
 You want this committee to have one boy
and one girl.
 How many different choices of committees
can you make?

Make a Tree Diagram
Choices of Officers: since there are 3 boys and two girls to choose
from, let’s identify the boys as B1, B2, and B3, and the girls as G1 and
G2.
B1
G1 G2
B2
G1
G2
How many combinations are there?
Just count the number of arrows!
B3
G1 G2
6 Ways!
Shortcut?
So if you count the ending outcomes,
there were 6 choices of pairs that could
talk to Ms. Langan.
 How could we get this number without
making a diagram? Is there a shortcut?
 Let’s try another example to find out.

Lindsey’s Closet
Lindsey is going to be late because she
can’t decide what to wear!
 She has a choice of 4 shirts, 3 pairs of
jeans, and 2 pairs of shoes.
 Let’s make a tree diagram to represent
this.

Put the largest # of choices on top
•Name some choices of outfits.
•Follow the choices down from the shirt
to the shoes.
•How many choices are there all
together? – Count the bottoms.
Let’s make a generalization…
3 boys and 2 girls = 6 combinations
 4 shirts, 3 jeans, 2 shoes = 24
combinations

THE COUNTING PRINCIPAL SAYS …
 If one event can occur in “m” ways and
another event can occur in “n” ways, then
then MULTIPLY ALL THE CHOICES
TOGETHER to discover the total number of
combinations!
Let’s Go Outback Tonight…
Ms. Bright’s sister works at Outback.
 When I go there, I have a choice of 4
different steaks, soup or salad, and 5
sides (garlic mashed potatoes, french
fries, baked potato, vegetables, or rice)
 How many different meals can I make?
 4 x 2 x 5 = 40 different steak meals
