Thinking, Fast and Slow is full of illustrative experiments and examples that you can even try on yourself!
Based on how System 1 and System 2 work as described in the previous nine chapters, Kahneman now goes into how these manifest into our biases.
The first bias discussed is our lack of feel for small sample sizes. System 1 creates a coherent story out of what it is presented, without allowing for doubts. As such, we tend to believe things to be absolutely true even when sample sizes are too small for us to be so confident. Examples used include:
1) The "hot hand" in basketball (which was proved statistically to be a fallacy) where it is believed that when a player is on a streak, he is more likely to hit the next shot.
2) The belief that higher rates of cancer in small towns is the result of special factors that we can determine. In fact, small towns have both higher and lower rates of cancer, because sampling is so low that random fluctuations create rate differences that appear significant.
3) The belief that smaller schools provide better educations. Smaller schools do show better results, but they also show worse results, due to the same sampling issue.
Kahneman also discusses anchoring, where he shows that even when we are confronted with a seemingly random number (such as through spinning a random roulette wheel), our brains use that number in coming to certain conclusions. Baffling! For example, list prices for houses have an effect on what even experts perceive as the value of the house. This process plays a role in negotiations, where certain skilled negotiators will try to get the adversary to anchor on a favourable number to them.
Finally, the availability bias is discussed. This causes us to believe in certain odds based on our own recollection of such incidences. Kahneman argues that this is the result of substitution, where we answer a different question when the original question is too hard. For example, when considering the percentage of Hollywood marriages that end in divorce, we are likely to overestimate as we substitute the question "How many Hollywood divorces can I recall being discussed?" Incidentally, this bias will also make you believe you are contributing more to things like your teams' accomplishments and your marital chores than your teammates and your spouse, respectively.