Chapter 21

Probability and Ambiguity

Taylor Kreiling

            One main part of this chapter was when Charles Sanders Peirce observed probability and its role in mathematics. This chapter talks a lot about the probability inside and involving triangles and circles. In the picture below the chapter talked a lot about the probability that a random chord is longer than a side of the equilateral triangle that is provided. It said that we now have a new process that shows that the sum of three perpendiculars corresponds to the length of the stick. Also what is the probability of you breaking a stick into 3 pieces and it ending up forming a triangle? Then it gave me two problems one about the breaking of a stick into three pieces and it forming a triangle. The problem took its solution from William Whitworth and the same answer will be found in many older textbooks on probability and it is entirely wrong!

           

            In this chapter it also talks about the three-prisoner problem and it compares it to the probability of picking a red card out of two black cards and one red card. This was kind of like what we learned in class, which I found much easier to understand.  It also talks about the three prisoners paradox and how in 1959 Richard E. Bedient had received many letters from other mathematicians saying his solution was invalid.

            Then it talked about the Monty hall problem that was used during the game show called “Lets make a deal”  it states that you should always pick a door. We talked about this in class as well which made it easier to understand the wording that was used in the problem.

            For my three references I picked D.H. Brown “The problem of three prisoners”, N. Starr “A paradox in probability theory” these two had to do with the three prisoners paradox. While I was reading these two references I noticed that they were very in detail using big words that were hard to understand that was one thing I disliked about both of those references that I’m glad the author didn’t add in the chapter. One thing I did like that the author added in the chapter was that he brought out little snippets of the reference that I could understand fully. For my other reference I picked A.H. Bohl, M.J.  Liberatore and R.L. Nydick “ A tale of two goats…and a car” This had to do with the Monty Hall problem that was in the chapter and also in class. The article talked a lot about more in depth parts of probability that lead to me being confused and lost within the reading forcing me to read it many times until I finally understood it enough to write about it. One thing that I liked that the author put in the chapter was when he explained how it was to your advantage to open a door and switch doors.

           Overall I really enjoyed this chapter and reading the references that I did although it was very confusing at times I enjoyed the reading and learned a lot from the chapter.