Chapter 41 had two main topics, induction and probability. I had a tough time wrapping my head around most of the topics throughout the chapter, but a couple were fairly easy to understand. The very first topic that was talking about was the patterned carpet. The patterns on the carpet were compared to the real world, since the patterns on the carpet are always changing. Just like how the patterns of the real world are not constant. After reading the first couple of paragraphs I was pretty confused, but this quote helped me understand the topic a lot better, "the patterns of the real world, as distinct from this imaginary one, are constantly changing, like a carpet that is rolling up at one end while it is unraveling at the other end."

 Like in our class, there were a lot of relevance to playing cards. The mathematicians used playing cards to prove some hypothesis'. One of the interesting ones was the one about cards with blue and green backs. One hypothesis stated that if you have three face cards with green backs, and two face cards with blue backs, then you are obviously more likely to pull a face card if you pick one with a green back. Another hypothesis stated that if you have three red cards with green backs, and to red cards with blue backs, then you are more likely to pull a red card if you pick a card with a green back. Both of these hypothesis were proven true. To take it a step further, you would think that if you wanted to pull and red face card, you would pick a card with a green back. However with the information the book gives us, this is not the case. There ends up being only one red face card with a green back, while there are two red face cards with blue backs, thus disproving ones initial thought. The chapter goes on with a bunch of different probability tricks involving, a women picking her husband, a man picking out with pie he should eat, pulling poker chips out of a hat, and another using spinners. 

I thought this chapter had some interesting, but confusing topics. What I thought was most surprising about the chapter was the part about the spinners. You can refer to the chapter to wee what the spinners look life. If you match up the spinner head to head to see which one get spinner gets the high number, then spinner A beats spinner B and spinner C, and spinner B beats spinner C. After looking at this data, you would think that spinner C is the weakest out of the three in every circumstance. However if you were playing against two other people to see who would get the number and you had your choice of spinner, you should pick spinner C. It turns out after some testing that spinner C is the best choice, and spinner A is actually the worst. I had to re-read this a couple times because at first I didn't think it made any sense. I found myself doing that for most of the chapter, because it was a lot of information to take in.