"Life is only good for two things; discovering mathematics and teaching mathematics." -- (Simeon Poisson) Caroline Herschel (1750-1848) and Mary Somerville were named as the first honorary female members of the Royal Astronomical Society. Herschel and her brother, William, are considered by some to be the founders of modern astronomy. Although Caroline was a equal partner in their many accomplishments - such as discovering many comets and nebulae - William received the lion's share of the credit, including being listed as the discoverer of the planet Uranus. Women were simply not considered equals in fields such as math and science. Caroline's honorary membership in the Royal Astronomical Society was bestowed upon her when she was 85 years old. Why did Herkimer think that tired people from the East would never make it to California? Answer: He heard that there was no west for the weary. Herky's friends: EDDIE KETT ... this guy was always very polite. TIM BURR ... a lumberjack. ASSIGNMENT #38 Reading: Review Chapter 6, as necessary. Also review results obtained by classroom activities. Exercises: Test 6A (Handout). Work out the problems and make sure you are familiar with the terms used. Answers will be posted.

You are working with ideas and concepts fromChapter 6.

The laws of probability are, for the most part,common sense. Here is a simple example illustrating the law

Prob(A|B) = Prob(A and B)/ Prob(B)

Consider a family with two children. The four possible (oldest,youngest) combinations are shown at the right.

What is the probability that the family has two girls if it is known that at least one of the children is a girl?

Each of four (oldest,youngest) combinations is equally likely to occur. If you know that at least one child is a girl, the eliminates the (boy,boy) combination, leaving three equally-likely combinations. In only one of these combinations do we find two girls. Hence, the desired probability is 1/3.

Symbolically, if we let A = the event "the family has 2 girls" and B = the event "at least one of the children is a girl," then we want Prob(A|B). This, according to the conditional probability formula is Prob(A and B)/Prob(B) = (1/4)/(3/4) = 1/3.

 Oldest Youngest GIRL GIRL GIRL BOY BOY GIRL BOY BOY

=======================================

Text:
The Practice of Statistics, by Yates, Moore, McCabe. New York,W.H. Freeman and Company, 1999. (ISBN 0-7167-3370-6)

Supplemental books:
The Cartoon Guide to Statistics, by Gonick and Smith. NewYork, HarperCollins Publishers, 1993. (ISBN 0-06-273102-5)
How to Lie with Statistics, by Darrell Huff. New York, W.W.Norton & Company, 1982 (ISBN 0-393-09426-X)