# Chapter 1 Introduction to probability

Probability is a concept that affects our everyday lives in more ways than we may think. We can think of a probability as the chance that something will happen. These types of considerations come up in our everyday lives regularly. For example: let's say you randomly ran into a friend at the supermarket yesterday. What do you think the chances of this happening would have been? Would your answer be different if you lived in a city of 100 people versus 1 million people? Or, would your answer change depending how regularly you shopped, for example once per month versus 5 times per week?

Or, let's say you invested \$100 in the stock market today. One could ask: what is the probability this investment will generate a positive return in one year from now?

Or, what is the probability a randomly selected student from this class receives a B for the subject?

There are many, many more examples to which we may apply the concept of probability. You may be able to think of some.

Here are some examples for which you might know the answer:

1. Suppose you tossed a fair coin. What is the probability the coin toss would result in a 'tail'? [Note: probabilities are always between 0 and 1].

2. Now suppose the coin was biased, so that the probability of the coin toss resulting in a 'tail' was 0.7. What would be the probability the coin toss would result in a 'head'?

3. Now suppose you rolled an unbiased, 6-sided die. What is the probability you would roll either a 1, 2, 3, 4, 5, or 6?

4. Again suppose you rolled an unbiased, 6-sided die. What is the probability you would NOT roll a 1, 2, 3, 4, 5, or 6?

1. 0.5
2. 0.3
3. 1
4. 0