Chapter 8 Practice Questions

1.  Twenty percent of the employees of a company are college graduates.  Of these, 75% are in supervisory position.  Of those who did not attend college, 20% are in supervisory positions.  What is the probability that a randomly selected supervisor is a college graduate?

2.  A bag contains 1 white ball and 2 red balls.  A ball is drawn at random.  If the ball is white then it is put back in the bag along with another white ball.  If the ball is red, then it is put back in the back along with another two red balls.

a) What is the probability of drawing the second ball that is red?

b) Find the probability that the second ball is red given that the first ball is white.

c) If the second ball drawn is red, what is the probability that the first ball was red?

3. Roll two fair dice

1. What is the probability they do not show the same number?  Use complementary set
2. What is the probability that the sum is 7?
3. What is the probability that the sum is not more than 3?

4.  In a study to determine frequency and dependency of color blindness relative to females and males, 1000 people were chosen at random and the following result were recorded:

a)      Convert the table to a probability table by dividing each entry by 1000.

b)      What is the probability that a person is a woman, given that the person is color-blind?

c)      What is the probability that a person is color-blind, given that the person is a male?

d)      Are the events color-blindness and male independent?

e)      Are the events color-blindness and female independent?

5.  A computer store sells three types of microcomputers, brand A, brand B and brand C.  Of the computers they sell, 60% are brand A, 25% are brand B, 15% are brand C.  They have found that 20% of the brand A computers, 15% brand B computers, 5% of brand C computers are returned for service during the warranty period.  If a computer is returned for service during the warranty period, what is the probability that it is a brand C computer?

6.  From the standard deck of 52 cards, what is the probability of obtaining a 5-cards hand:

a) of all five are diamond?

b) of 4 spades and 1 diamond?

7.  Do # 24 on page 438

8. a) In a 4 child families, what is the probability of having 2 girls and 2 boys?

b) Of having only one boy and 3 girls?

Study Guide Chp 8

1. Sample space, events, and definition of probability.

2. Probability function, empirical probability and equally likely assumption.

3. Sample space of a die, and a pair of dice from pg. 408.

4. Union, intersection, complement of events, and odds and the expansion of those formulas.  Refer to the question done in class and homework questions.

5. Know the difference between mutually exclusive events, and independent event, and dependent event. 

6. Conditional probability and Bayes’ Formula. 

For the exam you may have a note card on the formulas.

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.