As seen in the preceding example, the legal system recognizes that we can never have absolute certainty in legal matters. Instead, we operate with various degrees of uncertainty. Juries are instructed to dedde that someone is guilty of a crime when they are certain ''beyond a reasonable doubt." This standard was adopted because there is always some small amount of doubt that the accused may be innocent. Jurors are instructed to operate under a different level of doubt when they are dedding about guilt or innocence in a dvil case. In civil cases, they are told to deliver a verdict of guilty when the "preponderance of evidence" supports this dedsion. Thus, jurors are instructed to operate under two different levels of uncertainty when the case before them is either criminal or civil. They need to be more certain when deciding that an accused party is guilty in a criminal case than in a dvil ca se. 160

Probability is the study of likelihood and uncertainty. It plays a critical role in all of the professions and in most everyday decisions. All medical diagnoses and treatment decisions are inherently probabilistic, as are decisions made in business, college admissions, advertising, and research. Prob ability is the cornerstone of science; the laws of probability guide the interpretation of all research findings. Many of our leisure activities also rely on the principles of probability, most notably horse racing and card games. Every time you decide to take an umbrella, invest in the stock market, buy an insurance policy, or bet on a long shot in the Kentucky Derby, you are making a probability judgment. Other than the proverbial death and taxes, there is very little in life that is known with certainty. Because we live in a probabilistic world, critical thinking will require an understanding of probability.