Algebra 1 8 Feb 2011SILENTLYSILENTLY

Homework: Probablility test next classMake a Unit Summary Foldable:

Topics: Definition of probability Making a tree, making a list, making an area model Finding # of outcomes using the counting principal Permutations and combinations Experimental vs. Theoretical Probability

WARM UP: You roll two dice but to make it interesting, you change the numbers on each die. One die has the numbers: 1, 3, 5, 7, 9, 11. The second dies has the numbers: 1, 2, 3, 7, 8, 9

Make an area model to show the possible sums.P( sum 8) = P (roll a 1 on either die) =

ObjectiveStudents will use the counting principal to

determine the number of possible outcomes.

Homework Due TODAYP 2 and P 4: pg. 575: 8, 13- write basic information and show steps use A.B.E. for

13 eP5: pg. 574: 6 write basic info and show steps

Yesterday’s - Class work

Probability QuizTUTORING– Mon and Wed, 3 - 4

Need to make up quiz:P2: Classie

P4: Haley, Anis, Tyson

P5: Natasha, Jesus

COME IN TODAY, PLEASE- lunch or after school.

review

How many different student identification (ID) numbers can be assigned if an ID number consists of any two letters from the alphabet followed by any three digits?

____ ____ ____ ____ ____∙ ∙ ∙ ∙

what if letters and numbers can not be repeated?

How many different student identification (ID) numbers can be assigned if an ID number consists of two letters from the alphabet followed by three digits, and no repetition is allowed?

____ ____ ____ ____ ____∙ ∙ ∙ ∙

practice- think-pair-share

how many different ID numbers can be assigned if an ID number consists of any 6 digits and they can be repeated?

____ ____ ____ ____ ____ ____ =∙ ∙ ∙ ∙ ∙

How would the total number be different if numbers could not be repeated?

____ ____ ____ ____ ____ ____ =∙ ∙ ∙ ∙ ∙

P4—QuizP2 and P5– go over quiz

Do your best!Be respectful to your classmates… silence please.silence please.

When you are done, turn your quizover on your desk. You may silently work on your homework.

words to knowpermutation- an arrangement in which the order is important. ex: for letters a, b, c, there are the following permuations:

abc, acb, bac, bca, cab and cba.(pepperoni and onion is different than onion and pepperoni)

combination- an arrangement in which order is unimportant.ex. for letters a, b, c, there are the following combinations:

abc (ex. A tossed salad of lettuce, onion and carrots)(pepperoni and onion = onion and pepperoni)

You must consider whether or not repetition is allowed.

Counting Principle

If there are “a” ways to make a choice and for each of these, there are “b” ways to make a second choice, and so on.

The product a b c… ∙ ∙is the total number of possible outcomes.

permutation- example A pg.570You are redecorating your room and have five pictures to

arrange in a row along one wall. The pictures are labeled A, B, C, D and E.

1) how many ways can you arrange the five pictures?There are 5∙4∙3∙2∙1 or 120 different arrangements.

2) How many different ways can you arrange any 3 of the 5 pictures in random order?

There are 5∙4∙3 or 60 different arrangements.

We can write this in math notation as 5P5 = 120 read as“the number of permutations of 5 things chosen 5 at a time”

We can write this in math notation as 5P3 = 60 read as“the number of permutations of 5 things chosen 3 at a time”

practice1. The San Benito Boys and Girls Club basketball coach

has seven players dressed for a game.a. In how many ways can they be arranged to sit on the

bench?b. Five players are assigned to specific positions for the

game. How many different teams can the coach put on the floor?

c. What if Sam must always be the center? How many different teams can the coach put on the floor?

2. pg. 575, # 12

example c- pg. 572A piggy bank contains 6 coins: dollar, half-dollar, quarter, dime,

nickel and penny. If you turn it upside down and shake it, one coin will fall out at a time.

a) If you shake it until 3 coins come out, how many different sets of coins can you get?

This is a combination because the order of the coins in the piggy bank doesn’t matter. It is the same thing to have a nickel, dime and penny in the piggy bank as having a penny, nickel and dime.

We can see that there are 6∙5∙4 = 120 possible sets, but DNP = DPN = NDP = NPD = PDN = PND,

so we must divide 120 by 6.

We can write this in math notation as 6C3 = 20 read as“the number of combinations of 6 things chosen 3 at a time” 6C3 =

6 5 4 12020

3 2 1 6ways