Probability. Normal distribution

Probability is a fundamental branch of mathematics that is used to study and measure the possibility of a particular event occurring. It is based on the analysis of random situations and helps us to make informed decisions and predict outcomes.

Probability is expressed numerically between 0 and 1, where 0 means that the event is impossible and 1 means that it is certain to occur. For example, if we flip a coin, the probability of getting heads is 1/2, since there are two possible outcomes (heads or tails) and only one of them is the one we are looking for.

There are different methods to calculate the probability of an event, depending on the type of experiment or situation. Classical probability is used when all possible outcomes are equally likely. For example, if we have a standard deck of cards, the probability of drawing an ace is 4/52, since there are 4 aces in a total of 52 cards. Frequential probability is based on repeated observations. For example, if we roll a die 100 times and get a 3 on 20 occasions, the estimated probability of getting a 3 when rolling the die is 20/100, i.e., 1/5. Conditional probability is used when the probability of an event depends on another event having already occurred. It is denoted as P(A|B), which represents the probability that event A will occur given that event B has occurred. For example, if we have a bag with 5 red balls and 3 blue balls, the probability of drawing a red ball given that a blue ball has already been drawn is 5/8.

Probability is applied in many areas of life, such as gambling, finance, statistics, decision making and science in general. It allows us to assess risks, analyze data, predict outcomes and make informed decisions based on available information.