Transcript Using the Counting Principle to find Probability

Counting Principle
Mrs Patek has three pairs of capri pants, a black pair, a tan pair and a blue pair.
She also has two different T- shirts, one white and one pink. Make a tree diagram
to show all the possible outfits.
What is the probability you will select the black capri pant and the pink T- shirt when selecting an outfit at
random?
Lindsey flips a coin and rolls a number cube
at the same time. Draw a tree diagram
to display the possible choices.
What is the probability you will get a heads and an even number?
Draw a tree diagram to show all the possible outcomes for flipping a coin three
times.
1.) How many possible outcomes are there for flipping a coin three times?
2.) P(exactly two heads) 3.) P(one head)
4.) P(three tails) 5.) P(at least two tails)
Critical Thinking: What's the shortcut
for finding the total number of possible
choices?
Answer: Multiply the number of choices from each
category. This shortcut is called the
Counting Principle or Multiplication principle
2
coin
•
6
=
# cube
12 choices
Examples of the Counting Principle:
1.) Jordan has a choice of wheat bread or rye bread
and a choice of turkey, ham, or tuna for lunch.
How many possible sandwich choices are there?
•
bread
=
lunch meat
2.) Jimmy is buying a new car and has a different choices as to the options.
There are,
6 different exterior colors
2 interior colors
4-cylinder, 6-cylinder, or 8-cylinder engine
single CD or 6-CD player
How many different cars does Jimmy have to chose from?
•
•
•
=
Using the Counting Principle to find Probability
A combination lock has 20 numbers on its dial. To open the lock, you must have
the correct three number combination. What is the probability that you randomly
select the correct combination to a lock, if you select three numbers at random?
1.) Use the counting principle to find the number of possible combinations.
2.) Write the probability that you will select the correct combination?
Use the multiplication principle to find the total number of possible outcomes.
Then determine the probability of the event.
F
Spinner X
E
Spinner Y
B
D
G
C
H
A
B
1.) You spin spinner X two times. Find the probability of spinning a C, then a B.
2.) You spin spinner y two times. Find the probability of spinning an A, then a B.
3.) You spin spinner X and then spinner Y. Find the probability of spinning a G, then a B.
A
Demonstrate Understanding:
1.) An Italian restaurant offers small, medium and large calzones. The choices of fillings are
cheese, sausage, spinach or vegetable. How many different calzones can you order?
2.) There are four different flavors of ice-cream at Lynn’s Luscious Ice Cream shop
(vanilla, chocolate, strawberry and chocolate-chip). There are three different types
of sauce (caramel, chocolate and strawberry) How many different types of
sundaes are possible?
3.) Make a tree diagram to show the sample space for tossing a coin and
spinning a spinner with five equal sections that are numbered 1-5.
4.) P(heads, 2)
5.) P(tails, odd)