Section 9-3Fundamental Counting PrincipleHomework due Feb 8

Main idea: use multiplication to count outcomes and find probabilities

Vocabulary: fundamental counting principle

If you toss a coin you have 2 possible outcomes – heads or tails.

If you toss 2 coins you have 4 outcomes. (hh, ht, tt, th)

If you toss 3 coins you have 8 outcomes. (hhh, hht, hth, htt, thh, tht, tth, ttt)

If you toss 4 coins how many possible outcomes are there?

Using multiplication instead of a tree diagram to find the number of possible outcomes in a sample space is called the Fundamental Counting Principle.

Find the number of outcomes:

Find the total number of outcomes when a coin is tossed and a number cube is rolled.

Coin has 2 possible outcomes

Number cube has 6 possible outcomes

Using the fundamental counting principle:

2 * 6 = 12

There are 12 different outcomes.

Find the total number of outcomes when a number from 0 to 9 is picked randomly, and then when a letter from A to D is picked randomly.

Numbers have 10 possible outcomes

Letters have 4 possible outcomes

Using the Fundamental Counting Principle:

10 * 4 = 40

There are 40 possible outcomes.

The Fundamental Counting Principle can be used to find the number of possible outcomes and solve probability problems in more complex problems, when there are more than two events.

JEANS:

You are in need of new jeans. The Jean Shop sells young men’s jeans in different sizes, styles, and lengths, as shown in the table. Find the number of jeans available. Then find the probability of selecting a size 32x34 slim fit.

The Jeans Shop
Waist Size / Length / Style
30 / 30 / Slim fit
32 / 32 / Boot cut
34 / 34 / Loose fit
36
38

Number of jeans available :

Sizes * length * style = total

5 * 3 * 3 = 45

There are 45 different types of jeans to choose from.

There is only one favorable outcome of a 32x34 slim fit. So

The probability of randomly selecting a 32x34 slim fit is 1/45.

CLOTHING:

The table shows the shirts, shorts, and shoes in Jeremy’s closet. How many possible outfits – one shirt, one pair of shorts, and one pair of shoes – can he choose?

Shirts / Shorts / Shoes
Red / Beige / Black
Blue / Green / Brown
White / Blue
Yellow

Possible outfits =

Shirts * shorts * shoes = total outfits possible

4 * 3 * 2 = 24 outfits

CEREAL:

You have four kinds of cereal and two kinds of berries to put on the cereal. What are your cereal-berry choices? How many choices do you have? Complete the table and find the total possible outcomes

Cereal / Berry

Section 9-3Fundamental Counting PrincipleHomework due Feb 8