# Unit 6: Probability

Read chapters 13, 14 and 15 of FPP and do the following review exercises:
Chapter 13 (pages 234-236): 2, 4, 5, 6, 8, 9, 10
Chapter 14 (pages 252-254): 1, 2, 5, 6, 7, 8, 9, 10
Chapter 15 (page 261-263): 2, 3, 4, 5, 6, 8, 11

"Mathematics of a Lady Tasting Tea" by Sir Ronald A. Fisher, in Volume 3 of The World of Mathematics, edited by James Newman. Read through at least the "Stateent of Experiment" section and as much as you can of the rest. Its language is formal and archaic.
Document source: The website of the Autonomous University of Madrid

## Possible essay questions:

These reconstruct the mathematical part of the article:
• Out of eight cups of tea, how many ways are there to choose four of them?
• In view of your answer to the first question, what is the probability (both as a fraction and as a percent) that the lady would choose the right four (milk-first) cups, just by accident (assuming that she could not tell the difference at all)?
• Out of four milk-first cups and four tea-first cups, how many ways are there to choose three milk-first ones and one tea-first one?
• In view of your answer to the third question, what is the probability that, again just by accident, she would choose three milk-first and one tea-first cups?
• How many cups must she guess right to convince Fisher that she can really taste the difference? Do you agree with him?

## Midterm project: (counts as a computer project)

As you read the description of the final project, you will see that, for that project, you are required to write six sections, not including the bibliography and appendix sections. The assignment for this unit is to write the Discussion/Conclusions section for a project that has already been partly written. The first four parts of the report and the bibliography and appendix for that experiment are available here. As in your final project, the section you will write for this assignment describes the inferences you draw (or do not draw) from the data gathered and the statistical tests performed, concerning the questions raised in the Statement of the Problem and Background sections. It also lists some influences that might have affected the results and suggests things that might have been done (adjustments to the experiment, or completely separate experiments) for further study of the topic. (To acknowledge that your conclusion is not the last word on the subject, or even that your conclusion denies the result you expected to find, is not to your discredit. Rather, it indicates a scientifically honest frame of mind.) This section should probably be about 2-4 pages double spaced.