ABSTRACT
This chapter introduces the key concept of probability, its fundamental rules and properties, and discusses most basic methods of computing probabilities of various events.
Probability: its meaning and definition
The concept of probability perfectly agrees with our intuition. In everyday life, probability of an event is understood as a chance that this event will happen.
Example 2.1. If a fair coin is tossed, we say that it has a 50-50 (equal) chance of turning up heads or tails. Hence, the probability of each side equals 1/2. It does not mean that a coin tossed 10 times will always produce exactly 5 heads and 5 tails. If you don’t believe, try it! However, if you toss a coin 1 million times, the proportion of heads is anticipated to be very close to 1/2.
This example suggests that in a long run, probability can be viewed as a proportion, or relative frequency. In forecasting, it is common to speak about the probability of an event as a likelihood of this event to happen (say, the company’s profit is likely to rise during the next quarter). In gambling and lottery, probability is equivalent to odds. Having the winning odds of 1 to 100 (1:100) means that the probability to win is 0.01. It also means, on a relativefrequency language, that if you play long enough, you will win about 1% of the time.
