Previous tests will be returned to students as soon as they are graded.
Prepare for the test. Work problems from each section. Read the chapter and section summaries. Write down what you are doing. Draw the Venn diagram or the tree diagram for complicated situations. Ask questions on the blog. Take the practice test.
Here are some answers to even HW problems:
Problem 6.10 (a) S= {all numbers between 0 and 24}
(b) = {any whole number up to and including 11,000}
(c) S = {0, 1, . . . 12}
(d) S= {any dollar and cents amount up to [insert your maximum guess here]}
(e) S = {any positive or negative number}
Problem 6.12 Four outcomes for two coins: {HH, HT, TH, TT}, eight for three coins: {HHH. HHT, HTH, HTT, THH, THT, TTH, TTT}, and sixteen for four coins (do that one yourself!).
Problem 6.16 (a) YYY -0000 through YYY-9999 = 10,000 numbers. (b) YYY-ZXX-XXXX, each X having 10 possible numbers, except the number can't start with a 0 or a 1 meaning that Z has only 8 possible values, so this means 8 * 10^6 LESS the restricted numbers (911-xxxx, 411-xxxx, etc.)
Problem 6.20 P(moves to another class) = 1 - P(stays) = 1 - .46 = .54.
Problem 6.24 P(wins large battle) = .6, P(wins three small battles) = P(wins individual small battle)^3 = .8^3 = .512. Choose the strategy with the larger probability of occurring.
Problem 6.40
Venn diagram has two circles representing getting job A and getting job B.
Both jobs: intersection of the two circles, the overlapped part, the biscuit.
First but not second: the part of circle A that is not within circle B
Second but not first: the part of circle B that is not within circle A
Neither: the part that is in the background, in NEITHER circle.
Problem 6.44
P(W) = 856/1626
P(W given prof degree) = 30/74
These are not the same. so gender and professional degree are not independent
Problem 6.56
P(y <> x) = 1/8,
P(y > x) = 1/2,
P(y <> x) = P(y <> x) /P(y > x) = 1/4.
Problem 6.48: P(W) * P(Manager given W) = P(Woman AND Manager)
One pattern that shows up a lot is Marginal * Conditional = Joint
If you divide both sides by Marginal you get
Conditional = Joint / Marginal.
IFF means IF AND ONLY IF.
IFF P(A) * P(B) = P(both A&B), A and B are independent.
IFF P(A) = P(A given B), A and B are independent.
HW for Tuesday night: DO problems 6.33 and 6.48. Read 6.66 and be prepared to work the problem. Essential question: How do mathematical independence and our regular understanding of independence relate? The chapter 4 tests were returned today. HW for Monday night: 6.39, .40, .53, and .56. The problem we worked today in class was problem .65. You would be wise to work through this problem and problem .66.
Notes from Friday (11/30) are embedded in the purple sections below.
Conditional probability rules:
PLEASE NOTE THE CORRECTION! BLOGGER WON"T ACCEPT THE VERTICAL LINE SYMBOL!!!
P(A GIVEN B) = P(A and B)/P(B)
P(B GIVEN A) = P(A and B)/P(A)
so of course
P(B) P(A GIVEN B) = P(A and B), the joint probability of A and B. It may be helpful to think of it like cancelling factors in the numerator and denominator of a fraction EXCEPT that the result is the JOINT probability. Be careful.
P(A) P(B GIVEN A) = P(A and B), again, the joint probability of A and B.
These relationships can be represented in two-way tables, Venn diagrams, and tree diagrams. The count within a cell of a two-way table divided by the marginal total is a conditional probability. Likewise, the joint probability for that cell divided by the marginal probability is also the conditional probability.
Tree diagrams can be useful when you are trying to work the problems backwards.
I don't think that I made this clear in class today:
P(A) = P(A and B) + P(A and not B) = P(A)P(B given A) + P(not A) P(B given not A).
HW for the weekend is problems 6.44 and 45.
If A and B are independent, then P(A) = P(A GIVEN B) and P(B) = P(B GIVEN A).
Interpretation: If A and B are independent, then whether or not B happened has no relationship with whether A happened.
Likewise, if A and B are independent, then whether or not A happened has no relationship with whether B happened
Today we used a Venn Diagram, a two-way table, and a tree diagram to represent the outcomes and probabilities associated with throwing two strangely-marked dice. All of the methods yielded the same answer.
HW for Tuesday (11/27) night: Re-work the weird dice problem from the AP exam (the one with two dice, one has only 9s and 0s, the other has 11s and 3s.) This time, instead of using simulation, use formal probability rules and a tree diagram, table, or Venn diagram. Answer the question in complete sentences. For part B, reconcile the answer with the joint probabilities you found in part A. Figure out the guidelines in your own words that tell you whether a price/reward is fair.
Get the reading done! What are the big concepts?
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Sorry for the delay: just got home from KSU.
HW for Monday night, Nov 26: 6.19, 20, 21
plus. . .finish State of Fear.
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Add problems 6.24 and 6.25, due Monday, November 26.
Don't forget to read State of Fear.
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he complete list of HW problems due Tuesday: 6.9, 10, 12, 13, 16 (plus any others you feel like doing).
Don't forget to read State of Fear.
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Events that are mutually exclusive ARE NOT independent.
Addition principle: P(A or B) = P(A) + P(B) - P(A and B)
Multiplication principle: P(A) P(BA) = P(A and B), the joint probability.
When B and A are independent, P(BA) = P(B), A happening or not has not relationship to B happening, so P(A) P(B)=P(A and B). THAT IS ONLY WHEN THE EVENTS ARE INDEPENDENT.
Key vocabulary
parameter
sample space
event
probability
joint probability
independent
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This won't be so bad. The test will be Thursday, Dec. 6.
What are YOU doing to maximize your understanding of the material?
- Are you creating an outline of the chapter?
- Have you developed a glossary for the vocabulary and formulas?
- Have you worked all of the homework problems when assigned?
- Do you read the sections that relate to the homework?
- Are you part of a study group?
- Do you ask questions?
- Have you worked problems from a study guide?
- Have you worked the online quiz (see the link on the right panel of this blog)?
- Do you look for the similarities and differences in the ways data are processed?
- Do you work with problems long enough to understand why the formulas work the way they do?
- Have you made connections between current concepts and prior knowledge?
- Have you gone online to review concepts that you have forgotten?
Just "going through the motions" does not lead to the success that you desire in Advanced Placement courses. Take control of your learning.
Be safe.
Posts
12 comments:
Was Friday's homework: problems 10, 12, 13, & 16 (in chapter 6)?
...or to answer those questions on the blog?
The questions on the blog are not that type of question.
What exactly is our homework?
10,12,13,16 or 9,13,16a
Okay, that's what I figured. So are 19, 12, 13, & 16 the homework? I just want to make sure.
Hey, wait a minute. . . you are both in the same class! Why do you have two different assignments??? Perhaps we need to do ALL those problems.
I refer you again to the questions on the blog. Embrace the subject in light of this amiguity. I will have to check Mr. S's notes to find out for sure what he assigned, but that should not stop you from doing the homework. Don't let uncertainty slow you down.
im still confused is the hw for tmrw all the mentioned pblms???
Yes, all the listed problems: 9,10,12,13,16
This only adds 1-2 problems to what you did for HW over the weekend.
when do we have to read state of fear by
State of Fear is due Thursday, November 29.
There are MANY copies out there on the bookshelves of last year's students if you still haven't borrowed one. A lot of the students' parents also read the book. There should also be copies available at the public library. (It's even available on DVD, but I wouldn't recommend it because you miss out on the graphs.)
Please note that while the author seems to be taking a stand on the issue, and was widely reviled in Hollywood for it, his point has to do with HOW and WHY we believe claims, not WHAT we believe.
Also, there's some rich information in the Epilogue that I'm sure you won't want to miss. Don't "give it away"!
I was wondering what the difference between disjointed and independent were, and do you think you might be able to explain the P(A&B)/P(A) thing that we've talked about in class? I don't really understand it all that well.
Evan 1st
Disjoint means that there is no overlap in the events. It is the same as mutually exclusive. For instance, you cannot get heads and tails on the same flip of a coin, or odd and two on one roll of a die. These are disjoint events.
The P(A&B)/P(A) is the conditional probability of B given that A happens. Many of our recent homework problems were good examples of this, for instance the probability that a randomly-selected working person was a woman was 46% (P(W)). The probability that a randomly-selected working woman was a manager was 32% (P(M given W)).
The probability that a randomly-selected working person is a woman AND a manager is P(W & M) = .46 times .32.
Similarly, the probability that the randomly-selected point in the 1 x 1 square falls in the cross-hatched area was 1/8 (P(y<.5 & y>x)).
The probability that a point falls in the upper-left triangle within the box was 1/2 (P(y>x)).
The probability that the point falls in the cross-hatched area GIVEN that it fell in the upper triangle is (1/8) / (1/2) = 1/4 (P(y<.5 & y>x)/P(y>x) = P(y<.5 given y > x)).
This is a very important part of the chapter.
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