Reading Update:

 The Drunkards Walk by Leonard Mlodinow

Chpater 3

Chapter three covers quite a bit of history and a few specific examples. Here it is in summary:

• Gerolamo Cardano existed and, more importantly, pioneered the idea that possible outcomes of a situation could be thought of as points in space (or coordinates)
• This chapter covers three probability problems:

1. You flip two coins, what is the probability that at both will heads? The answer is 25%. There are four possible outcomes of the flip: (heads, heads), (heads, tails), (tails, heads), and (tails, tails). There is a 25% chance that both or neither coins will be heads and a 50% chance that just one will be heads. The other question addressed is this: Assuming one coin will be heads, what is the probability of both coins being heads? Is it 50%? No. The condition that one of the coins will be heads only removes one of our four possible results (tails, tails). The statement does not state explicitly which coin is heads, so it could either be (heads, tails), (tails, heads), or (heads, heads). Therefore, the chances that both will be heads, knowing one of them will for sure be heads, will be 1 in 3, or about 33%.
2. The next problem is a joke I read last week involving some college students that missed an exam due to returning late from a road trip. They appealed to their professor claiming they had a flat tire. The professor issued the exams in different rooms and, in an attempt to catch the students lying, wrote the question, “which tire was flat?" on the second page of the exam. What is the probability that they answer the same tire? The correct answer is one in four. This is because there are four tires for them to choose. Check out the table. The chance that they choose the same tire is 4 in 16, or 1 in 4.
3. Now for the most fun one, the Monty Hall problem. This one has been around for some time and has caused quite a bit of humiliation for many many Ph.D.s as you will see later. Here is the problem as submitted by Craig Whitaker to Marilyn von Savant's column in PARADE magazine: 

Suppose you're on a game show, and you're given the choice of three doors. Behind one door is a car, behind the others, goats. You pick a door, say #1, and the host, who knows what's behind the doors, opens another door, say #3, which has a goat. He says to you, "Do you want to pick door #2?" Is it to your advantage to switch your choice of doors?

The answer is yes! I will not take the space to explain why, but you can see this -- and the humiliation of numerous mathematicians-- on Marylin's website here. 

And that is about it for chapter 3. I will keep you up to date with what else I learn in this book