Math Studies Dos

Sorry it took me so long to post this. I don't have a problem for guys but if I think of one if i can actually understand what I'm doing I'll post it up. So for now, here are the notes for today.

Agenda:
I. Find Correlation Coefficient
II. Mastering Calculator
III. Your Math Project

Objective: Students will be able to find the correlation coefficient using calculators.

On your calculator go to STAT. Click on No.1: Edit. Type in the numbers below.

L1: 2, 7, 12, 4, 9, 20, 8, 3, 32
L2: 7, 20, 32, 16, 27, 58, 5, 10, 104

Once done exit out pressing 2nd then Mode. Click on STAT then go right for CALC. Click on No. 1: 1-Var Stats, press ENTER again.

X Bar should equal and rounded to 10.78.

Next hit 2nd and ENTER. Now click 2nd and 2 for L2. Press ENTER.

X Bar should equal 31.

Next press STAT then EDIT. Highlight L3. Type in L1(2nd and 1) minus 10.78. L3(1) should now equal -8.78.

Next highlight L4. Type in L2(2nd and 2) minus 31. L4(1) should now equal -24.

Next highlight L5. Type in L3(2nd and 3) times L4(2nd and 4). L5(1) should now equal 210.72.

Clear Screen(2nd and Mode) then click clear.

Now press 2nd then STAT. Go to the right to MATH. Press No. 5 for sum. Sum(L5(2nd and 5)). You should get 2396. Divide that by 9 for the number of data. Press ENTER. You should now get 266.2.

Once again press 2nd then STAT. Go to the right to MATH. Press No. 5 for sum. Sum(L4(2nd and 4) squared). Press ENTER. You should get 8114.

Again press 2nd then STAT. Go to the right to MATH. Press No. 5 for sum. Sum(L3(2nd and 3) squared). Press ENTER. You should get 745.6 round to 746.

Now square root 8114 divided by 9. You should get 30.
Again square root 746 divided by 9. You should get 9.1.

Now multiply 30 and 9.1. The answer should be 273.

R= 266.2 divided by 273. Which equals .975. Square that to get .95 as your answer.

I really don't get this part here so yeah.

Press 2nd and 0. Go down to DiagnosticOn Press ENTER and ENTER again. It should say done.

Go to STAT then go to the right for CALC. Go down to No.4 for LinReg(a+b). Press ENTER and ENTER again.
y=a+b
a=3.213710879
b=-3.636661699
r2=.948983395
r=.9741577875


HOMEWORK IS ON PAGE 582. THE PROBLEMS ARE 1-4.

Math Studies 2

Septmeber 27, 2010

Bell Ringer
John has a 10% chance of solving a math problem.
Kate has a 20% chance of solving a math problem.
Joan has a 30% chance of solving a math problem.

If these chances are independent what is the probability that the problem will be solves if they work together?

Agenda
1. Bell Ringer
2. Correlation of 2 variables.
3. using variables in analysis.

Objective: students will be able to construct and evaluate a 2 variable scatter plot.

Big Picture: Two variable analysis allows a person to see patterns in data that may indicate a relationship.

Question

Shawnelle has a 13% chance of solving an art problem.

Rosanna has a 26% chance of solving an art problem.

Jack has a 90% chance of solving an art problem.

If these chances are independent what is the probability that the problem will be solves if they work together?

Review Set 14A

1. Donald keeps record of the number of clients he telephones over a consecutive period of days.
a. for how many days did the survey last?
b.estimate Donald's chances of telephoning:
i) no clients in a day
ii) four or more clients on a day
iii). less than three clients on a day

a. 1+6+12+9+6+3+2=39 total number of days
b. i). 1/39
ii). 6+3+2=11/39
iii). 1+6+12=19/39
2. David conducted a survey to determine the ages of people walking through a shopping mall. the results are shown in your book. find , correct to 3 decimal places the estimated probability that the next person David meets in the shopping mall is:
a. between 20 and 39 years of age
b. less than 40 years of age
c. at least 20 years of age

a. 45/112=0.4017~0.402
b. 45+19=64/112=0.5714~0.571
c. 45+37+11/112 or 112-19/112=93/112=0.8303~0.830
3. A farmer fences his rectangular property into 9 rectangular paddocks:
If a paddock is selected at random,what is the probability that:
a. it has no fences on the boundary of the property
b. it has one fence on the boundary of the property
c. it has two fences on the boundary of the property?

a. 1/9 because all but one is on a boundary
b. 4/9
c. 4/9
4. When a box of drawing pins dropped on to the floor it was observed that 47 landed on their backs and31 landed on their sides.Find correct to 2 decimal places,the estimated probability of a drawing pin landing:
a. on its back
b. on its side

47-Back, 31-Side
78 total number of pins
a. 47/78=0.602~0.60
b. 31/78=0.397~0.40
5. A saw mill receives logs of various lengths from a plantation. the length of a log is important in being able to produce timber of the length required.the following data indicates the lengths of at least100 logs received.
a. what is the probability of a log being less than 11 metres long arriving at the saw mill?
b. What is the probability of a log being longer than 15 metres arriving at the saw mill?
c. in the next batch of 50 logs how many would be expected to be between 11 m and 15 m long?

a. L < 11=3+4+14/100=21/100
b. L > 15=7+8/100=15/100
c. 11< L < 15=12+18+20+14=64/2=32 per 50 logs
6.At peak hour railway crossings are closed 30% of the time. If you have to drive through three railway crossings during peak hour, what are the chances you will have to stop at least once?

o-open=.7, c-closed=.3
Possible combination's
ooo-.7*.7*.7=.343
ooc
occ
coo
coc
cco
ccc

1-P(ooo)
1-.343=0.657
7.In a golf match, Annette has a 70% chance of hitting the green when using a nine iron and Kari has a 90% chance when using the same club. If, at a particular hole,they both elect to use a nine iron to play to the green, determine the probability that:
a. both hit the green
b. neither hits the green
c. at least one hits the green
d. only Anette hits the green

a..7*.9=.63
b. .3*.1=.03
c. 1-P(of no one)
1-.03=.97
d. .7*.1=.07
8. Jar A contains 3 white and 2 red marbles. Jar B contains 6 white and 4 red marbles. A jar is selected at random and then two marbles are selected WITHOUT replacement. Determine the probability that:
a. both marbles are white
b. two red marbles are picked from Jar A

Jar A: 3 whites, 2 red
Jar B: 6 whites, 4 red
a. Jar A- 1/2*3/5*2/4=6/40
Jar B- 1/2*6/10*5/9=30/180
6/40+30/180=19/60 (add because they're independent)
b. 1/2*2/5*1/4=2/40

QUESTION OF THE DAY

If P(C)= .10 P(D)= .3 and P(C U D)= .11 are C and D independent events?

BELL RINGER

A{Q, R, S, T, U, V} B{T, U, V, W, X, Y, Z}

1. How many elements are in {A}? n{A} = 6
2. How many elements are in {B}? n{B} = 7
3. how many elements are in {AuB}? n{AuB} = 10 because T, U, V are in both sets, so they are only counted once
4. How many elements are in {AnB}? n{AuB} = 3 because T, U, V are in both sets
5. Are these two sets independent or dependent? These sets are dependent because they overlap over elements T, U, V

AGENDA
1. Bellringer
2. Homework Review
3. Independent probabilities

OBJECTIVE
Students will learn to identify independent probabilities

HOMEWORK
Begin review set A on pg. 490. Remember to ask questions tomorrow for the test on Thursday.

QUESTION
P(G)=0.3, P(D)=0.7 and P(GuD)= 1, are G and D dependent or independent?


I know, horrible question... Sorry this was so late. My computer has a virus or something so i would get half done and it would crash, leaving me to start over... Hooray for attempt number 11! Yay!

hey

guys I just got my username

September 20, 2010

Bell Ringer

1: If the probability of an Event E is 40%, what is the probability of not E? (E')

2: If the same event E takes place 3 times, what is the probability of the result being

E E' E' ??

1. Probability of E is 40% = 4/10 ....which leaves the probability of E' to be 6/10.

6+4= 10

2. k so its really hard to do a tree diagram, but that would be the best step so, time to go to plan B which iiissss...just explaining it.... ok so

• first we have to calculate the probability of E which is 4/10
• then, we know that the probability of E' is 6/10
• again, we know that the probability of E' is 6/10
• So now we can MULTIPLYYYYY

4/10 * 6/10 * 6/10 = 8/125

So the answer for the probability of E E' E' is 18/125

Agenda

I. Bell Ringer

II. Theoretical vs. Experimental Probability

III. Independent Events (in other words... h.w..we got tricked! =] )

Homework!!

pg. 490 #1-5

OBJECTIVE

Students will be able to differentiate the difference between experimental and theoretical Probability.

Question of the day....drum roll please!!!!

1.The probability that Blazer will spend the day with a Princess is 80%. What is the probability that Blazer won't spend the day with the Princess?

2. Over three days, what is the probability that Blazer will spend the first two days with the princess and not on the third day? (P P P' )

September 16, 2010

Agenda

1) Bell Ringer
2) Homework review
3) Independent Events
4) Review for Quiz

Objective: Students should be able to identify dependent and independent events and calculate probability accordingly.

Bell ringer( we went over it in class)

	Biology	Physics	Chemistry	Total
Male	40	16	35	91
Female	15	24	20	59
Total	55	40	55	150

1) P(M)= 91/150
2) P(M) ∪ P(C)= 91+20/150 = 111/150
3) P(P) ∩ P(M)= 16/91

Homework Review
During class, we went over question 6 from page 483.

You are supposed to draw a venn diagram to solve the problem. (I'm so sorry- I tried many different ways to copy my venn diagram from microsoft word but it won't work.)

The venn diagram has two circles
1st circle is labeled Mu for mumps and the 2nd circle is labeled as Me for Measles.
The part where the two circles overlap(in the middle) is labeled as Me and Me because it contains both
So, here are the values
Mu= 2
Me=12
Mu and Me(middle)= 12
Outside the circle but inside the box (neither mu or me)= 4
All these values add upto 30.

a) P(Mu)= 14/30
b) P(Mu) - P(Mu ∩ Me)
24/30 -14/30 = 2/30
(you don't have to reduce it because IB doesn't expect you to reduce it on the exams)
c) P(Mu' ∪ Me')= 4/30
d) P(Mu ∩ Me)/ P(Mu)= 12/14

Tomorrow's Quiz
- probability question including chart, tree diagram, and venn diagram.

September 23, 2010: Chapter test for Chap. 14.

Practice question:

Out of 30 kids, 20 love strawberry and chocolate, 24 love chocolate and 23 love strawberry.

a) How many kids love neither of the flavors mentioned above?
b) What is the probability that a kid loves chocolate ONLY?
c) What is the probability that a kid loves chocolate given he loves strawberry?
d) What would you pick? Strawberry or Chocolate? :)

Hey everyone :)
I'm so sorry for not posting the venn diagram :\ I really tried to for the past hour but it didn't work. If you have any questions about today's blog, please let me know. I will be more than glad to help you out! I hope the practice question was easy. Do not forget- we have a quiz tomorrow!!!
Have a blessed day guys.

Lillian Sangha

Math Studies II

AGENDA:

I) Bell Ringer

II) Venn Diagrams to evaluate probability

III) Math Studies Project Timeline

I) Bell Ringer

80 students were asked what type of television program they watched the previous night.

35 - watched sports (S)

50 - watched drama (D)

42 - watched news (N)

10 - watched all 3 programs

7 - watched sports and news only

12 - watched news and drama only

14 - watched sports and drama only

*Draw a Venn diagram of the above problem.

SOLUTION:

* To solve the problem it would be good to follow the letters:

a) 10 goes into center of all 3 circles as everyone watched it.

b) 7 goes between sport and news

c) 12 goes between news and drama

d) 14 goes between sports and drama

e) To find "e", we have to add all the numbers that are included in "sport circle" which is red color, and that includes ( a)10 + b)7 + d)14 + e)? = 35, as 35 students watched sports program.

10 + 7 + 14 + E = 35

31 + E = 35

E = 4

------------------------------------------------

*We do the same procedure with drama:

To find "F" we need to add: a)10 + c)12 + d)14 + f)? = 50

10 + 12 + 14 + F = 50

36 + F = 50

F = 14

------------------------------------------------

*And News:

To find " G" we need to add: a)10 + b)7 + c)12 + g)? = 42

10 + 7 + 12 + G = 42

29 + G = 42

G = 13

--------------------------------------------------------------------

*After completing those three subproblems we will obtain this:

However, this isn't the and of the problem, because we have to find h. To find it, we first have to add all the numbers, and they should add up to 80. a) 10 + b)7 + c)12 + d)14 + e)4 + f)14 + g)13 + h)? = 80

10 + 7 + 12 + 14 + 4 + 14 + 13 + H = 80

74 + H = 80

H = 6

*Here is the final solution:

Some Classwork:

1) The probability that the student is boy in P.E. = 37/70

2) The probability that boy GIVEN English = 10/18

3) The probability Math GIVEN boy = 12/42

4) The probability Girl GIVEN P.E. = 15/35

OBJECTIVE:

Students will be able to use Venn diagrams to solve probability problems.

HOMEWORK:

IB Math Studies Book Page 483,#4-7.

QUESTIONS:

1) In IB classes there are 52 students. 30

students love Math, 10 ART,and 15 TOK.

3 students like Art and Math

2 students like Math Art and TOK

1 student like Art and TOK

5 student like Math and TOK.

Find out how many students like Math alone, Art and TOK and how many students, if any, don't like any of the subject.

2) Which group are You in?

Math Math Math.. (I forgot the name of the lesson)

BELLRINGER

Create a decision tree for:

Probability it will snow is .75
If it snows, the probability that I will ski is .9
Probability I will ski if it doesn't snow is .2
Find the Probability that I will ski


ANSWER: 29/40


SOLUTION:



Ski .9
/
.75 Snow
/ \
/ .1 No Ski
/
.25 No Snow /-- .2 Ski
/ \/
/
.8 No Ski


To find the probability of skiing you:

1. Multiply the .75 probability of snow X the .9 of skiing if there's snow which equals .675 and put into fraction form is 27/40.
2. Multiply the .25 probability of no snow X .2 of skiing without snow and that equals 2/40.
3. Multiply the .1 probability of not skiing with snow X .75 of snow which equals 3/40.
4. Multiply one last time the .25 probability of no snow X not skiing without snow and that equals 8/40.
5. Then you add 27/40 + 2/40 and that equals 29/40, which is the probability you will ski.



AGENDA

I. Bell Ringer
II. Review Homework
III. Probability w/ Venn Diagram
IV. Schedule for Math IA




Objective:
Student will be able to use Venn Diagram to illustrate real world situations and find a probability.




Question:
Bob lives in a house. Everytime it rains heavily his basement floods and he has to take out buckets of water. Probability it will rain heavy is .4. Probability it won't rain is .6. Probability he won't take out buckets of water if there's no rain is .6.
What is the probability he will take out buckets of water?



Ahh. I know this is a little late.. I barely got home half an hour ago. Easiest question I could come up with.. lol.
Have fun. The tree looked better before I posted it.

September 13, 2010

BELLRINGER (which was confusing)

Create a tree diagram given 2 archers Li and Yuka. Li has a 3/4 probability of hitting. Yuka has a 4/5 probability of hitting. Show all possible outcomes for each making two shots at target.

SOLUTION:

H STANDS FOR HIT

M STANDS FOR MISS

LI

/ \

3/4 H 1/4 M

/ \ / \

4/5 H 1/5 M 4/5 H 1/5 M

/ \ / \ / \ / \

3/4 H 1/4 M 3/4 H 1/4 M 3/4 H 1/4 M 3/4 H 1/4 M

/ \ / \ / \ / \ / \ / \ / \ / \

4/5H 1/5M 4/5H 1/5M 4/5H 1/5M 4/5H 1/5M 4/5H 1/5M 4/5H 1/5M 4/5H 1/5M 4/5H 1/5M

Possible Outcomes: (Start left, work your way down)

When Li First Hits it

1. 3*4*3*4 = 144/400 (H,H,H,H)

2. 3*4*3*1 = 36/400 (H,H,H,M)

3. 3*4*1*4 = 48/400 (H,H,M,H)

4. 3*4*1*1 = 12/400 (H,H,M,M)

5. 3*1*3*4 = 36/400 (H,M,H,H)

6. 3*1*3*1 = 9/400 (H,M,H,M)

7. 3*1*1*4 = 12/400 (H,M,M,H)

8. 3*1*1*1 = 3/400 (H,M,M,M)

When Li First Misses

9. 1*4*3*4 = 48/400 (M,H,H,H)

10. 1*4*3*1 = 12/400 (M,H,H,M)

11. 1*4*1*4 = 16/400 (M,H,M,H)

12. 1*4*1*1 = 4/400 (M,H,M,M)

13. 1*1*3*4 = 12/400 (M,M,H,H)

14. 1*1*3*1 = 3/400 (M,M,H,M)

15. 1*1*1*4 = 4/400 (M,M,M,H)

16. 1*1*1*1 = 1/400 (M,M,M,M)

AGENDA

I. Bell Ringer

II. Sample Space

III. Independent vs Dependent Events

OBJECTIVE

Students will be able to use tree diagrams to show sample space and define independent and Dependent Events

HOMEWORK

IB Math Studies Book Page 488 #s 9, 10 , 11

Question to Answer (if you want, remember you have to answer 2 each week)

Lucia goes to lunch. She can either choose white or chocolate milk. And for the snack she can choose between chocolate and sugar cookies. List ALL of her possible outcomes.

Just a fun question, which combination would you pick and why?

:) . This took forever, i hope you guys understand and enjoy. see you guys i have to go now.