5 - Fundamental Counting Principle

basic
P.O.D. #5
At DiNardo’s Cafe, customers
must choose between
regular or decaf coffee. They
can also order their coffee
hot, iced or frozen. What is
the probability that the next
customer will order a regular
iced coffee?
Sample Space:
RH, RI, RF, DH, DI, DF
Probability: P(RI) = 1
6
advanced
Mr. Coleman is purchasing new
uniforms for the track team. Below are
the color options for the uniforms. If he
chooses randomly, what is the
probability that he will choose a yellow
shirt, blue shorts, and white shoes.
Shirts Shorts Shoes
Orange Red
White
Yellow
Blue
Teal
Green
Sample Space:
ORW, ORT, OBW, OBT, YRW, YRT,
YBW, YBT, GRW, GRT, GBW, GBT
Probability: P(YBW) = 1
12
Fundamental Counting Principle
The Fundamental Counting Principle states that
the total number of outcomes in a compound
event can be found by multiplying the number of
outcomes of each event.
Example:
Use the Fundamental Counting Principle to find
the total number of outcomes when a coin is
tossed and a number cube is rolled.
Coin
Cube
Total
2  6 = 12
One
Two
Three
Four
Five
Six
Heads
H1
H2
H3
H4
H5
H6
Tails
T1
T2
T3
T4
T5
T6
Example:
Find the total number of outcomes from rolling a number
cube and choosing a letter from the word NUMBERS. Then
find the probability of rolling a 6 and choosing an M.
Cube
Word
Total
1
P(6M) =
42
6
×
7
=
42
Whiteboard:
How many outcomes are possible when rolling a
number cube and picking a marble from 4 different
colored marbles?
Cube  Marble = Total
6  4 = 24
Whiteboard:
Find the number of different outfits that can be
made from 3 sweaters, 4 blouses, and 6 skirts. Then
find the probability of randomly selecting a
particular sweater-blouse-skirt outfit. Is the
probability of this event likely or unlikely?
Sweater  Blouse  Skirt = Total
3  4  6 = 72
1
P(outfit) =
72
This event is unlikely to happen.
Let’s keep practicing:
Pg. 761/120 worksheet
P.O.D. #6
basic
How many outcomes are possible when
spinning the spinner to the right, rolling a
number cube and flipping a coin three
times?
Spinner Cube
8
•
6
Coin Coin
•
2
•
2
Coin
•
There are 384 possible outcomes
2
=
384
Take out Friday’s HW:
Pg. 761/120 worksheet
Let’s keep practicing:
BIM pg. 425-426 #1-26 all