Mood:  rushed

Hello Class:

Remember there will be no DLA during the final week.  Therefore complete them as soon as possible.  They are due on Dec2.

Thank you and Happy Thanksgiving.

Mood:  quizzical

Q: How do you know when or which formula to use?

A:  Always draw the tree first.  

for two branches case:

1. If the question is conditional: it will ask for the probability of the second branch given the first branch

Read question #38 in 8.3

2. If the question is Bayes: it will ask for the probability of the first branch given the second branch.  ( Reversal )

Read question #25 in 8.4.

For #40 draw the same tree as it was in the class.

Again the question asks for the same color given :

two possibility it could be all red or all white.  

Conditional probability:

P(R2/R1)  = P(R2 and R1) / P (R1)

P(W2/W1) = P(W2 and W1) / P(w1)

Same as in #38 this is a dependent event try to rewrite the above formula.

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With replacement

P( same color) = (2/7) (2/7) + (5/7) (5/7) = 29/49

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For B: without replacement

Same reasoning as above:

P(same color) = (2/7) (1/6) + (5/7)(4/6) = 11/21

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For #38, draw the tree diagram as was drawn in class.

Thought process:

This is the conditional probability since it ask for given that :...........

Conditional prob. 

First, given it is red

P(R2/R1) = P( R2 and R1) /  P(R1)

Second scenerio, given it is white

P(R2/W1) = P(R2 and W1) / P(W1)

Since this is a dependent event we have:

P(R2 and R1) = P(R1) •P(R2/R1)

P(R2 and W1) = P(W1)  • P( R2/W1)

In essence, the question ask for drawing a red ball on the second draw.

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Therefore:

P(R2) = (2/7) (2/7) + (5/7) (2/7) = 2/7

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For part B.  draw the tree as it was drawn in class.

same thought process as it was in part a.

P(R2) = (2/7)(1/6) + (5/7) (2/6) = 2/7

Now, try to ponder why is the answer the same?  Try to make up your own tree and answer the question as it was in #38.

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1. Start studying now, after Thanksgiving break the week will go by fast.

2.  Ask questions.

3. Organize your study materials.

4. Make the note cards.

5. Practice make perfect.

6. Think positive, nothing is impossible for those who try their hardest.

7. Hope for the best.

8. God speed!

Happy Thanksgiving class!

The Final exam will be given on:

December 16, 2009 from 4 pm to 6:50 pm.

The exam will cover chapter 1 through chapter 9.  Calculators can be used during the final.

Final Exam for Math 37:

Monday December 14 at 10:40 am to 1:15 p.m in the same room.

If people do not believe that mathematics is simple, it is only because they do not realize how complicated life is.  ~John Louis von Neumann

Mathematics are well and good but nature keeps dragging us around by the nose.  ~Albert Einstein
 

Arithmetic is where numbers fly like pigeons in and out of your head.  ~Carl Sandburg, "Arithmetic"
 

So if a man's wit be wandering, let him study the mathematics; for in demonstrations, if his wit be called away never so little, he must begin again.  ~Francis Bacon, "Of Studies"
 

 The essence of mathematics is not to make simple things complicated, but to make complicated things simple.  ~S. Gudder

Halmos, Paul R.

I Want to be a Mathematician, Washington: MAA Spectrum, 1985.

Don't just read it; fight it! Ask your own questions, look for your own examples, discover your own proofs. Is the hypothesis necessary? Is the converse true? What happens in the classical special case? What about the degenerate cases? Where does the proof use the hypothesis?
I Want to be a Mathematician, Washington: MAA Spectrum, 1985.

Hardy, Godfrey H. (1877 - 1947)

[On Ramanujan]
I remember once going to see him when he was lying ill at Putney. I had ridden in taxi cab number 1729 and remarked that the number seemed to me rather a dull one, and that I hoped it was not an unfavorable omen. "No," he replied, "it is a very interesting number; it is the smallest number expressible as the sum of two cubes in two different ways."
Ramanujan, London: Cambridge Univesity Press, 1940.

Reductio ad absurdum, which Euclid loved so much, is one of a mathematician's finest weapons. It is a far finer gambit than any chess play: a chess player may offer the sacrifice of a pawn or even a piece, but a mathematician offers the game.
A Mathematician's Apology, London, Cambridge University Press, 1941.

I am interested in mathematics only as a creative art.
A Mathematician's Apology, London, Cambridge University Press, 1941.

  Niels Bohr 

Profession: physicist. Born 1885, Copenhagen, Denmark. Died 1962, Copenhagen, Denmark.

Hi Class:

The DLAs are due on December 2, 2009.  Anyone who turn in the DLAs early will get 2 extra points.

For those of you who are absent, I distribute the weekly practice sheet on Wednesday in class.  If you need those practice sheet now, please email me and I will send you the practice problems via email.  

Hello Class:

Please remember to complete your DLAs and have a nice weekend.

They are due Wednesday on December 2.  There will be no DLA on the final week.  Therefore, complete them as soon as possible no exception.